Question

Javier has a model of a cone with a radius of 3 inches and a height of 10 inches. Javier increased his model’s volume by doubling its radius and height. What is the volume of the larger cone in cubic inches?

Answer 1

240 pi in. ^2

Explanation:

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Tisa B Sora

Answer 2

`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)`