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A cube with sides 5 cm has the same volume as a cone with height 3 cm. Find the exact value of the radius of the base of the cone.

(I need the steps please)

User Thamar
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Let's call the radius of the base of the cone "r". The volume of the cube is (5 cm)^3 = 125 cm^3. The volume of the cone is given by the formula (1/3)πr^2h, where h is the height of the cone, which is 3 cm. Setting these two volumes equal to each other, we have:

(1/3)πr^2 * 3 = 125

Expanding and solving for r, we have:

πr^2 * 3 = 375
πr^2 = 375 / 3 = 125
r^2 = 125 / π
r = √(125 / π)

So the exact value of the radius of the base of the cone is approximately equal to √(125 / π) cm
User Ahsanwarsi
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