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
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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​.

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​.

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

 

 

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