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prisoha [69]
3 years ago
11

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 doublin

g its radius and height. What is the volume of the larger cone in cubic inches?
Mathematics
2 answers:
yan [13]3 years ago
8 0

Answer:

240 pi in. ^2

Step-by-step explanation:

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

Thank you

Tisa B Sora

statuscvo [17]3 years ago
3 0

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}

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