Question

A cylinder with a radius of 12cm and a height of 20cm has the same volume as a cone with a radius of 8cm. What is the height of the cone

Answer 1

Answer: 135cm

Step-by-step explanation

Volume of a cylinder = πr²h

Volume of a cone. = 1/3πr²h

The two shapes are both solid shapes.

Since the have same volume, we can then equate the two together and solve for the height of the cone.

Now make H the height and R the radius of the cylinder and h the height and r the radius of the cylinder.

Now equating the two

πR²H = 1/3πr²h

Now substitute for the values now

Multiply through by 3

3πR²H = πr²h

But π is common so it could be obliterated from the equation

3R²H = r²h

3 x 12² x 20 = 8² x h

3 x 144 x 20 = 64 x h

60 x 144 = 64h

8640. = 64h

Therefore

h = 8640/64

= 135cm