Mathematics: The cones are similar. find the volume of cone b. write your answer in terms of pi.

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The cones are similar. find the volume of cone b.

MyaMya12

10.03.2022

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

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

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

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

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