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The volume of a cone varies jointly as its height, and the square of its radius. If a cone with a height of 8 cm and a radius of 2 cm has a volume of 33.5 cm3 what is the volume of a cone with a height of 6 cm and a radius of 4 cm?

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The volume of a cone with a height of 6 cm and a radius of 4 cm is:

V =  100.5 cm³

What is the volume of a cone with a height of 6cm and a radius of 4cm?

If the volume of a cone varies jointly as its height, and the square of its radius, then we can write the equation:

V = R²*H*k

Where:

R = radius

H = height

k = constant of the variation.

Here we know that if R = 2cm and H = 8cm, the volume is 33.5 cm³, then we can replace that to get:

33.5 cm³ = (2cm)²*8cm*k

The value of k is:

(33.5 cm³)/(  (2cm)²*8cm ) = k = 1.046875

Then the formula for the volume is:

V = R²*H*1.046875

Now if the radius is 4cm and the height is 6cm, the volume will be:

V = (4cm)²*(6cm)*1.046875 = 100.5 cm³

If you want to learn more about cones:

https://brainly.com/question/1082469

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