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

Answer:

240 pi in. ^2

Step-by-step explanation:

Just took the test. Correct me if I'm wrong!

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Tisa B Sora

Answer 2

Answer:

$240 \pi\ in^{3}$

Step-by-step 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

$z^{3}=\frac{x}{y}$

In this problem we have

$z=2$ -----> scale factor

substitute

$2^{3}=\frac{x}{y}$

$8=\frac{x}{y}$

$x=8y$

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

Find the volume of the original cone

$V=\frac{1}{3}\pi r^{2} h$

we have

$r=3\ in$

$h=10\ in$

substitute

$V=\frac{1}{3}\pi (3^{2})(10)=30 \pi\ in^{3}$

therefore

The volume of the larger cone is equal to

$8*30 \pi\ in^{3}=240 \pi\ in^{3}$