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
