Question

A solid is in the form of a right circular cylinder with a hemisphere at one end and a cone at
the other end. The radius of the common base is 8 cm. and the heights of the cylindrica
and conical portions are 10 cm and 6 cm respectivly. Find the total surface area of the
solid. [use = 3.14]​

Answer 1

Given :

• common base radius = 8 cm
• height of cylinder = 10 cm
• height of conical portion = 6 cm

To find :

• Total surface area of the solid

Formula used :

▶ Curved surface area of cone

$\boxed{\sf{CSA\:of\:cone=\pi (radius)\times(slant\;height)}}$

▶ Curved surface area of Cylinder

$\boxed{\sf{CSA\:of\:cylinder=2\pi (radius)\times(height)}}$

▶ Curved surface area of Hemisphere

$\boxed{\sf{CSA\:of\:hemisphere=2\pi (radius)^2}}$

▶ Pythagoras theorem to find the Slant height of right circular cone

$\boxed{\sf{(hypotenuse)^2=(height)^2+(base)^2}}$

Solution :-

Finding the slant height of Right circular cone of height 6 cm and base radius 8 cm

Using pythagoras theorem

$\implies\sf{(slant\;height)^2=(8)^2+(6)^2}$

$\implies\sf{slant\:height=10\;cm}$

Finding the Curved surface area of cone

$\sf{CSA\:of\:cone=\pi (radius)\times(slant\;height)}$

$\sf{CSA\:of\:cone=3.14\times8\times10=251.2\:cm^2}$

Finding the Curved surface area of cylinder

$\sf{CSA\:of\:cylinder=2\pi(radius)\times(height) }$

$\sf{CSA\:of\:cylinder=2\times3.14\times(8)\times(10)=502.4\;cm^2}$

Finding the CSA of Hemisphere

$\sf{CSA\:of\:hemisphere=2\pi (radius)^2}$

$\sf{CSA\:of\:hemisphere=2\times3.14\times8\times8=401.92\:cm^2}$

Finding the total surface area of Solid

$\implies\sf{TSA\:of\:solid=CSA\:of\:cone+CSA\:of\:cylinder+CSA\:of\;hemisphere}$

$\implies\sf{TSA\:of\:solid=251.2+502.4+401.92 \;\; cm^2}$

$\underline{\boxed{\red{\implies \sf{TSA\:of\:solid=1155.52\;\;cm^2}}}}$