Question

The cones are similar. Find the volume of cone B. Write your answer in terms of pi.

Answer 1

Answer:

The volume of cone B is equal to $256\pi\ ft^{3}$

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

The scale factor is equal to the ratio of its diameters

so

16/8=2

step 2

Find the volume of cone B

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z -----> the scale factor

Vb ----> volume of cone B

Va ----> volume of cone a

$z^{3}=\frac{Vb}{Va}$

we have

$z=2$

$Va=32\pi\ ft^{3}$

substitute

$2^{3}=\frac{Vb}{32\pi}$

$Vb=(8)(32\pi)=256\pi\ ft^{3}$

Answer 2

The volume of cone B that is similar to cone A is calculated as: 256π ft³.

How to Find the Volume of Similar Solids?

Volume of Solid A/volume of solid B = a³/b³, where a and b are the corresponding linear measures of both solids.

• Volume of cone A = 32π ft³
• Radius of cone A = 8/2 = 4 ft
• Volume of cone B = B
• Radius of cone B = 16/2 = 8 ft

32π/B = 4³/8³

B(4³) = (8³)(32π)

64(B) = 16,384π

B = 16,384π/64

Volume of cone B is: 256π ft³

Learn more about the volume of similar solids on:

https://brainly.com/question/16599646

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