Two different right cones are being considered by a design team to hold one liter (1000

cubic centimeters) of oil. Design A has a height that is double the diameter of the base.

Design B has a height that is triple the diameter of the base. Which design has a smaller

surface area? What percent less is that surface area?

Answers

Answer 1

Answer:

The surface area of Design A is smaller than the surface area of Design B.

The area of Design A is 94.65% of the Design B.

Step-by-step explanation:

The area of a right cone is given by the sum of the circle area of the base and the lateral area:

[tex] A = \pi r^{2} + \pi rL [/tex]   (1)

Where:

r: is the radius

L: is the slant height  

The slant height is related to the height and to the radius by Pitagoras:

[tex] L^{2} = H^{2} + r^{2} [/tex]  

[tex] L = \sqrt{H^{2} + r^{2}} [/tex]    (2)

By entering equation (2) into (1) we have:

[tex] A = \pi r^{2} + \pi r(\sqrt{H^{2} + r^{2}}) [/tex]  

Now, let's find the area of the two cases.

Design A: height that is double the diameter of the base, H= 2D = 4r

[tex] A_{1} = \pi r^{2} + \pi r(\sqrt{(4r)^{2} + r^{2}}) = \pi r^{2}(1+ \sqrt{17}) [/tex]  

The volume of the cone is:

[tex]V = \frac{1}{3}\pi r^{2}H[/tex]

We can find "r":

[tex] V = \frac{1}{3}\pi r^{2}(4r) = \frac{4}{3}\pi r^{3} [/tex]

[tex] r = \sqrt[3]{\frac{3V}{4\pi}} = \sqrt[3]{\frac{3*1000}{4\pi}} = 6.20 cm [/tex]

The area is:

[tex] A_{1} = \pi (6.20)^{2}(1+ \sqrt{17}) = 618.7 cm^{2} [/tex]  

Design B: height that is triple the diameter of the base, H = 3D = 6r                  

The radius is:

[tex] r = \sqrt[3]{\frac{3V}{6\pi}} = \sqrt[3]{\frac{3*1000}{6\pi}} = 5.42 cm [/tex]  

The area is:

[tex]A_{2} = \pi r^{2} + \pi r(\sqrt{(6r)^{2} + r^{2}}) = \pi r^{2}(1 + \sqrt{37}) = \pi (5.42)^{2}(1 + \sqrt{37}) = 653.7 cm^{2}[/tex]  

Hence, the surface area of Design A is smaller than the surface area of Design B.

The percent of the surface area of Design A is less than Design B by:

[tex] \% A = \frac{618.7 cm^{2}}{653.7 cm^{2}}\times 100 = 94.65 \% [/tex]

Therefore, the area of Design A is 94.65% of the Design B.

                         

I hope it helps you!


Related Questions

Help plzz need the answer and that explanation plz don't send a file I need help with question 21!! thx so much

Answers

Answer:

No, they cannot be becuase the points are too different- no same numerical

values.

Step-by-step explanation:

Oliver has created a plot of his backyard on the given coordinate plane, so that each unit length is one yard. He wants to design a right triangular plant bed for his backyard that has an area of eight square yards. After placing one vertex of the base of the plant bed at (3, 8) and one vertex at (7, 8) on his coordinate plane, he has to determine where to place the last vertex. Locate the possible locations of the last vertex on the coordinate plane.

Answers

Answer:

The possible locations are;

(3, 4), (3, 12), (7, 4), and (7, 12)

Please find attached the plot of the points created with Microsoft Excel      

Step-by-step explanation:

The given parameters of the plot of Oliver's backyard are;

The area of the right triangular plant bed Oliver wants to design, A = 8 yd²

The length of a/each unit of the plot = 1 yard

The location of one of the vertex of the right triangular area = (3, 8)

The location of the other vertex of the right triangular area = (7, 8)

We note that the area of a triangle, A = 1/2 × Base length, B × Height, h

Let the distance between the two plotted point represent the base length, 'B', therefore;

B = 7 - 3 = 4 (We subtract only the x-values (7 and 3) given that the y-values (8 and 8) are the same;

Therefore, the base length, B = 4 yards

A = 1/2 × B × h

∴ A = 8 yd.² = 1/2 × 4 yd. × h

h = 8 yd.²/ 2 yd. = 4 yd.

The height of the right triangle, h = 4 yd.

Therefore the possible locations of the last vertex the right triangle on the coordinate plane, given that the first two points are parallel with the x-axis, are points 4 units above or the y-axis value of the plotted points with the x-value of the last vertex being either 3, or 7 as follows;

(3, 8 ± 4) or (7, 8 ± 4) which give points, (3, 4), (3, 12), (7, 4), and (7, 12).

Answer:

3,4 7,4

Step-by-step explanation:

Margo wants new carpet and a new wallpaper border for her bedroom. The room is 5.7 yards long and 6 7 8 yards wide. About how many square yards of carpet will she need? About how many yards of wallpaper border will she need?

Answers

Answer:

39.19 yards^2

25.15 yards

Step-by-step explanation:

To determine the squares square yards of carpet needed, we have to determine the area of the room

The room is shaped like a rectangle

area of a rectangle = length x breadth

5.7 x 6 7/8

To multiply, convert 6 7/8 to a  decimal

to do this, divide 7 by 8. Add the value gotten to 6

5.7 x 6.875 =39.19 yards^2

To determine the yards needed for the border, calculate the perimeter of the room

Perimeter = 2 x (length + breadth)

2 x(5.7 + 6.875) = 25.15 yards

Can someone please help me on this problem?

Answers

Answer:

$5820.07

Step-by-step explanation:

Substitute 243 into the equation for n:

[tex]c=117\sqrt[3]{243^{2} }+1264\\c=117\sqrt[3]{59049}+1264\\c=117*38.9407384+1264\\c=4556.06639+1264\\c=5820.06639[/tex]

Round 5820.06639 to the nearest hundredth:

5820.07

$5820.07

who ever answer this get a brainliest and a thank you i need it answered asap

Answers

Answer:

a = 9

Step-by-step explanation:

For solve the problem we can use the Pythagorean theorem in this way

a^2 + (3√3)^2 = (6√3)^2

If we solve the equation we have

a^2 + 27 = 108

a^2 = 81

a = +/-9

we take only the the positive value because a length can’t be negative

a = 9

At a publishing company 60% of the editors are female.
30% of the female editors and 20% of the male editors have a maths degree.
What percentage of all the editors have a maths degree?

Answers

0.3 percent because 50% of 60% is 0.3%

32 km 24 km What is the length of the hypotenuse? C = kilometers ​

Answers

Answer:

40 kilometers

Step-by-step explanation:

the hypotenuse is a² + b² = c²

so first we have to get 32 and 24 into ²

            32² = 1024       (32 × 32)

            24² = 576         (24 × 24)

1024 + 576 = 1600

now we need to find the square root of 1600

√1600 = 40     (calculator)

therefore, the hypotenuse is 40 kilometers

goodluck, hope this helped,

-cheesetoasty

HELP MEEEEEEEEE I REALLY DONT KNOW THIS ONE

Answers

Answer:

[tex]volume = \pi {r}^{2} h \\ = \pi( {5}^{2} ) \times 6 \\ 150\pi \: cubic \: units[/tex]

Answer:

471

Step-by-step explanation:

Using Pi=3.14

First find the area of the bottom circle:

3.14*([tex]5^{2}[/tex])

=78.5

Then multiply the result by the height

78.5*6=471

therefore,

Volume of clylinder: 471 units squared

Please give me brainliest if corrrect :)

Jesse has a storage container in the shape of a right rectangular prism. The volume of the container is 43.875 cubic meters, the length is 5 meters and the width is 3.9 meters.

Answers

Note: Consider we need to find the height of the container.

Given:

The volume of container in the shape of right rectangular prism = 43.875 cubic meters.

Length = 5 meters.

Width = 3.9 meters.

To find:

The height of the container.

Solution:

We know that the volume of a rectangular prism is:

[tex]V=l\times w\times h[/tex]

Where, l is length, w is width and h is height.

Putting [tex]V=43.875,l=5,w=3.9[/tex] in the above formula, we get

[tex]43.875=5\times 3.9\times h[/tex]

[tex]43.875=19.5\times h[/tex]

[tex]\dfrac{43.875}{19.5}=h[/tex]

[tex]2.25=h[/tex]

Therefore, the height of the rectangular container is 2.25 meters.

f(x) = 3 x e^2x
That's the problem​

Answers

Answer:

6 e (*2)x

Step-by-step explanation:

i hope this helps and the 2 is a square unit

Answer:

y = 0

Step by step explanition:

1. A signal tower has two lights that are 30 feet apart from each other, one directly above the other. From

a boat, the angle of elevation of the lower light is 14 degrees, and the angle of elevation yo the upper

light is measured to be 32 degrees.

a) Find to the nearest foot the distance from the boat to the lower light.

b) The boat and the foot of the tower are in the same horizontal plane. Find to the nearest foot the

distance from the boat to the foot of the tower.

Answers

Solution :

It is given that the distance between the two lights is 30 feet.

The angle of elevation of the upper light from the boat, ∠ ABP = 32 degree

The angle of elevation of the lower light from the boat, ∠ ABQ = 14 degree

∴ ∠ PBQ = ∠ ABP - ∠ ABQ

              = 32 - 14

              = 18 degree

In triangle PAB

∠ PAB = 180 - (90 + 32)

           = 58 degree

Similarly in triangle AQB

∠ AQB = 180 - (90 + 14)

           = 76 degree

Now considering triangle PBQ and applying the sine theorem,

[tex]$\frac{PQ}{\sin 18}=\frac{BQ}{\sin 58}$[/tex]

we know PQ = 30 feet

∴ [tex]$BQ =\frac{\sin 58}{\sin 18} \times 30$[/tex]

        = 82.33 feet

Again taking the right triangle ABQ and applying sine theorem,

[tex]$\frac{BQ}{\sin 90}=\frac{AB}{\sin 76}$[/tex]

[tex]$\frac{82.33}{\sin 90}=\frac{AB}{\sin 76}$[/tex]

∴ [tex]$AB = 82.33 \times \sin 76$[/tex]

         = 79.88 ft

         = 80 feet

 

HELPP!!!!!!!!!!!!!!!!

Answers

Answer:

D.4 3/4

Step-by-step explanation:

hope it helps you

Lines CD and DE are tangent to circle A shown below: Lines CD and DE are tangent to circle A and intersect at point D. Arc CE measures 112 degrees. Point B lies on circle A. If Arc CE is 112°, what is the measure of ∠CDE? (4 points) Question 5 options: 1) 124° 2) 136° 3) 68° 4) 56°

Answers

Answer:

Option (3)

Step-by-step explanation:

By the theorem, angle between two tangents intersecting each other outside the circle is half of the difference between intercepted arcs.

From the figure attached,

Two tangents CD and DE are intersecting each other at point D outside the circle A.

Two intercepted arcs are minor arc CE and major arc CBE,

Measure of arc CE = 112°

Therefore, measure of major arc CBE = 360° - 112°

                                                               = 248°

m(∠CDE) = [tex]\frac{1}{2}(\text{arcCBE}-\text{arcCE})[/tex]

                 = [tex]\frac{1}{2}(248-112)[/tex]

                 = [tex]\frac{1}{2}\times 136[/tex]

                 = 68°

Option (3) will be the correct option.

Answer:

C

Step-by-step explanation:

please help me with this math problem, the question is on the picture that i attached, ill mark brainliest if the answer is correct. NO links!

Answers

Answer:

5/12

Step-by-step explanation:

Think SohCahToa

Soh- Sin: opposite/hypotenuse

Cah- CoSin: adjacent/hypotenuse

Toa- Tan: opposite/adjacent

Opposite: The length on the opposite side of the angle.

Adjacent: The length next to the angle.

Hypotenuse: The longest side of the angle.

A square pyramid has a volume of 297 cubed feet. The width and length of the pyramid are
both 9. feet. Find the height of the pyramid.

Answers

Answer:

11

Step-by-step explanation:

H =V/(LxW)/3

H = 297/(9x9)/3

H = 297/(81)/3

H = 297/27

H = 11

Therefore, the height of the pyramid is 11ft square

A graph of f(x) = 6^2 - 11x + 3 is shown on the grid
What are the zeros of f?

A. 3
B. 2 and 9
C. 11/12
D. 1/3 and 3/2

Answers

The answer is D
Use Conects

-2x+6y=12 x-3y=3 graph the equations

Answers

Answer:

here ya go bruv:

Step-by-step explanation:

:3

Answer:

The graph, with the answers, is in the picture below.

Step-by-step explanation:

−2x + 6y = 12

Slope:  [tex]\frac{1}{3}[/tex]    y-intercept: (0, 2)

LINE COLOR: RED

x − 3y = 3  

Slope:  [tex]\frac{1}{3}[/tex]   y-intercept: (0, −1)

LINE COLOR: BLUE

I want its solution and the unit is about algebraic fraction.

Answers

Answer:

3x²/(3x - 9y)

This should be the simplest form.

Step-by-step explanation:

Combine the fractions:

(5x² - 2x²)/((6x - 6y) - (3y - 3x))

Combine like terms:

3x²/(6x - 3x - 6y - 3y)

Solve.

3x²/(3x - 9y)

Answer:

9x^2      

======

6(x - y)

Step-by-step explanation:

Begin by switching the - to a plus. Switch the x and y in the second denominator.

5x^2              2x^2

=====      +    ======

6x - 6y          3x - 3y

Pull out the common factors in both denominators. Use the distributive property.

5x^2              2x^2

=====      +    ======

6(x - y)          3(x - y)

Multiply both the numerator and denominator by 2 on the left had fraction.

5x^2              2*2x^2

=====      +    ======

6(x - y)          2*3(x - y)

5x^2                4x^2

=====      +    ======

6(x - y)          6(x - y)

Put both numerators over a common denominator. Notice that the + sign shifts up.  It shifts up because both fractions have been changed to a common denominator.

5x^2        +        4x^2

===================

          6(x - y)

Combine the two numerators since they are of the same power.

9x^2      

======

6(x - y)

help pleaseeee i dont get this also show work

Answers

Answer:

AC = 2

BC = [tex]2\sqrt{2}[/tex]

CD = 4

CF = 4

BD = [tex]2\sqrt{2}[/tex]

DE = 8

EF = [tex]4\sqrt{2}[/tex]

DF = [tex]4\sqrt{2}[/tex]

Step-by-step explanation:

Since all of these are isosceles triangles, it means both legs of every triangle are congruent to each other. So,

Given: AB = 2

Find:

AC = AB = 2

BC = [tex]2\sqrt{2}[/tex]

CD = 4

CF = CD = 4

BD = BC = [tex]2\sqrt{2}[/tex]

DE = 8

EF = [tex]4\sqrt{2}[/tex]

DF = EF = [tex]4\sqrt{2}[/tex]

does anyone know the answer?? i’ll mark brainlists

Answers

I’d say D as the answer

Ten times the square of a non zero number is equal to fifty times the number.

What is the number?

Answers

Answer:

5

Step-by-step explanation:

10x^2=50x

10x=50

x=5

x=5 hsjsbseinsosnsiwnskdbisndisnsdjd

Find the product of (2a+b)^2

Answers

Answer:

(2a+b)^2

4a^2 + 4ab + b^2

product=4

Answer:

4a²+b²+4ab

Step-by-step explanation:

(2a+b)²=(2a)²+(b)²+2×2a×b

(a+b)²=a²+b²+2ab

answer:- 4a²+b²+4ab

find the slope, y-intercept. write the equation :).

Answers

y=mx+b
m=2/5
b= y-intercept witch is 4

y=2/5x+4

slope: -4/5

y-int: 4

y=-4/5x+4

It costs Eduardo 2 d 3 dollars to go to the carnival for d days. How many dollars does the carnival cost if Eduardo goes for d 5 days?

Answers

Answer:

$250

Step-by-step explanation:

Given:  Cost for d days carnival = $2d^3 .....(i)

where d is number of days

Now we have to calculate the total cost incured for 5 days of carnival

we can simply put d = 5 in above equation (i)

= 2×5^3 = 2×125 = $250.

Therefore carnival cost if Eduardo goes for d 5 days = $250

I need help finding the answer!

Answers

Answer: x=4

Step-by-step explanation:

Since this is a rectangle we already know that all the angles are 90, so we can do this:

46+10x+4=90

50+10x=90

10x=40

x=4

is the Square root of 18 divided by 3 a rational or irrational number? explain using full sentences

Answers

Answer:

irrational

Step-by-step explanation:

[tex]\sqrt{18}[/tex] = [tex]\sqrt{9}[/tex] · [tex]\sqrt{2}[/tex] which is the same as 3[tex]\sqrt{2}[/tex]

3[tex]\sqrt{2}[/tex] divided by 3 equals [tex]\sqrt{2}[/tex], which is irrational

pls help with this !!

Answers

Answer:

25.12 so the nearest 10 is 25.10

If side 1 is 13, side 2 is 12, and side 3 is 18, can a triangle be made?

Answers

Answer:

no

Step-by-step explanation:

I need more answers and I don’t know how to make an account

Answers

Answer:

Well if your on chrome book sign out and select add person and make your new email and password and you have a new account.

Step-by-step explanation:

Hope this helps and have a wonderful day!!!

Answer:

Account for what, brain ly

Step-by-step explanation:

step 1: Go to sign up

step 2: create a email

step 3: create password

Classify the triangle with the given side lengths: 5, 9, 10

Answers

This can be a right triangle
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