Mathematics: Two similar cones have volume of 343pi cubic centimeters and 512pi cubic centimeters. The height of each cone is equal to 3 times its radius. Find the radius and height of both cones

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Two similar cones have volume of 343pi cubic centimeters

Ответ:

jessicaortiz6

26.01.2022

Mathematics

For the first cone: r = 7 cm, h = 21 cm

For the second cone: r = 8 cm, h = 24 cm

Step-by-step explanation:

The volume of the first cone is $343\pi cm^3$

The volume of the second cone is $512\pi cm^3$

We are told that the height of each cone is 3 times its radius, hence:

h = 3r

The volume of a cone is given as:

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

Substituting h = 3r:

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

For the first cone, V = $343\pi cm^3$ , radius, r, will be:

$343\pi = \pi r^3\\\\\\= r^3 = 343\\\\\\r = \sqrt[3]{343} \\\\\\r = 7 cm$

∴ Its height will be:

h = 3r = 3 * 7 = 21 cm

For the second cone, V = $512\pi cm^3$ , radius, r, will be:

$512\pi = \pi r^3\\\\\\= r^3 = 512\\\\\\r = \sqrt[3]{512} \\\\\\r = 8 cm$

∴ Its height will be:

h = 3r = 3 * 8 = 24 cm

The radius and height of the first cone are 7 cm and 21 cm respectively while the radius and height of the second cone are 8 cm and 24 cm respectively.

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Two similar cones have volume of 343pi cubic centimeters and 512pi cubic centimeters. The height of each cone is equal to 3 times its radius. Find the radius and height of both cones

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