d Problem9: A combined solid made up of a radius 3 cm and length h cm and a hemisphere with the same radius as the cylinder has volume 792 cm cube . find the value of h​. | Job Exam Rare Mathematics (JEMrare) - Solved MCQs

# Solution:

Here radius and height of the solid is described — it is a obviously a cylindrical shape solid!

We know the volume of a cylinder of radius ‘r’ and height ‘h’ is given by the formula:

$V = π r 2h$

So, if we put values or ‘r’ and Pi here we get;

$V=(3.14)(3)^2h$

or

$V=29.26 h cm^3$—-1

Now,

Volume of hemisphere = 2πr3/3

$Vs=\frac{2(3.14)(3)^3}{3}$

$Vs=56.52cm^3$ —–2

Adding equations 1 & 2, we get;

$V+Vs=29.626h+56.52$——3

Now as per statement, if cylindrical solid and sphere is combined, i-e

$V+Vs=792cm^3$

Putting this value of V+Vs in eq 3, we get;

$792=29.26h+56.52$

So,

$735.48=26.29h$

$h=\frac{735.48}{29.26}=25.14cm$

So, the height of the solid is 25.14cm