Question

A solid is composed of a cylinder with a hemisphere at one end and a cone at other end as shown in the figure. If the radius of each of these solids is 7 cm and height of the cylinder is equal to slant height of the cone, find the total surface area of the solid if slant height is 4 cm.

Answer 1

For all figures,

$r=7cm$

$l\left(slantheight\right)=h\left(heightofcylinder\right)=4cm$

T.S.A of the figure= C.S.A of Cone+C.S.A of cylinder +C.S.A of hemisphere.

CSA of cone: $\pi rl=\left(3.14\right)\times \left(7cm\right)\times \left(4cm\right)=87.92c{m}^2$

CSA of cylinder: $2\pi rh=\left(2\right)\times \left(3.14\right)\times \left(7cm\right)\times \left(4cm\right)=175.84c{m}^2$

CSA of hemisphere: $2\pi r^2=\left(2\right)\times \left(3.14\right)\times (7cm{)}^2=307.72c{m}^2$

Adding all: TSA of figure= $571.48c{m}^2$