Question

A solid is in the shape of a cone surmounted on a hemisphere,the radius of each of them is being 3.5 cm and the total height of solid is 9.5 cm.Find the volume of the solid. $(Use\pi =3.14)$

Answer 1

Solution:

As per the data given in the question, we have

Radius of the hemisphere = 3.5 cm = R

Radius of the cone = Radius of the hemisphere = 3.5 cm = R

Total height of the solid = 9.5 cm = H

Then,

Length of the cone = Total height – Radius of the cone

L = 9.5 – 3.5 = 6 cm

Now,

The volume of the cone = V₁ = $\frac{1}{3}\times \pi R^{2}L=\frac{1}{3}\times \pi \times {3.5}^2\times 6-----\left(1\right)$

The volume of the hemisphere = V₂ = $\frac{2}{3}\times \pi R^3=\frac{2}{3}\times \pi \times 5^3-----\left(2\right)$

Total volume of the solid = Volume of the cone + Volume of the hemisphere = V

V = V₁ + V₂

V =$\frac{1}{3}\times \pi \times {3.5}^2\times 6+\frac{2}{3}\times \pi \times 5^3$

V = 166.75 cm³

So, the volume of the solid = V = 166.75 cm³