Cone volume?

Question

A drinking cup is made in the shape of a right cone, with an open top of 7.5cm and a height of 4.3cm. If the height of the

cup is increased by 1centimeter, then what happens to its volume?

Answer 1

Volue of the right cone (V) = 1/3∏r^2h.

So, Volume is directly proportional to height.

Means that : V α h.

If h increases, then volume also increases.

V = 1/3∏r^2h = 1/3∏r^2h.           < --- Current volume
V1 =1/3∏r^2(h + 1)                     < --- Increased volume
V1 - V = 1/3∏r^2h + 1/3∏r^2 -1/3∏r^2h = 1/3∏r^2.
Volume increases by 1/3∏r^2.

From the given data : 2∏r = 7.3.

r = 3.75/∏.

So, volume increases by 1/3∏(3.75/∏)^2 = 1.492.