2 Answers

Amarachi · Answer 1 · 2020-04-15T19:45:15+0000

Answer:

$240 \pi\ in^(3)$

Explanation:

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

x-----> the volume of the larger cone

y-----> the volume of the original cone

z^(3)=(x)/(y)

In this problem we have

z=2 -----> scale factor

substitute

2^(3)=(x)/(y)

8=(x)/(y)

x=8y

That means-----> The volume of the larger cone is 8 times the volume of the original cone

Find the volume of the original cone

$V=(1)/(3)\pi r^(2) h$

we have

$r=3\ in$

$h=10\ in$

substitute

$V=(1)/(3)\pi (3^(2))(10)=30 \pi\ in^(3)$

therefore

The volume of the larger cone is equal to

$8*30 \pi\ in^(3)=240 \pi\ in^(3)$

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