WAEC - Mathematics (2024 - No. 32)
A cone and a cylinder are of equal volume. The base radius of the cone is twice the radius of the cylinder. What is the ratio of the height of the cylinder to that of the cone?
5: 4
4: 3
3: 2
3: 4
Wyjaśnienie
Vol of cylinder = \(\pi\)r\(^2\)H = vol of cone = \(\frac{1}{3}\)\(\pi\)r\(^2\)h
H = height of cylinder and h = height of cone
Let y = radius of cylinder = y, then radius of cone = 2y
\(\pi\)y\(^2\)H = \(\frac{1}{3}\)\(\pi\)(2y)\(^2\)h
y\(^2\)H = \(\frac{1}{3}\)4y\(^2\)h ( \(\pi\) cancels out and cross multiplying)
The ratio of the height of the cylinder to that of the cone = \(\frac{\text{H}}{\text{h}}\) = \(\frac{4y^2}{3y^2}\)
= \(\frac{4}{3}\) = 4: 3 (y\(^2\) cancels out )