Question

Write the total surface area of a right circular solid cone having radius 10 cm and slant height 25 cm (Take$\pi = \dfrac{{22}}{7}$).
$
  {\text{A}}{\text{. }}1100c{m^2} \\
  {\text{B}}{\text{. }}2100c{m^2} \\
  {\text{C}}{\text{. 1}}150c{m^2} \\
  {\text{D}}{\text{. 1}}200c{m^2} \\
 $

Answer 1

Hint: Here we go through by first finding the curved surface area of the right circular cone by applying the formula, curved surface area$ = \pi rl$ and then add the surface area of the bottom to find out the total surface area of the cone.

Complete step-by-step answer:

Here in the question it is given that,
Radius(r) =10 cm and Slant height (l) = 25cm
We know that curved surface area$ = \pi rl$ where r= Radius and l= Slant height
$\therefore $ Curved surface area$ = \pi rl = \dfrac{{22}}{7} \times 10 \times 25 = 785.71c{m^2}$
Now we find the base area which is circular by the formula $\pi {r^2}$.
Area of base circle=$\pi {r^2} = \dfrac{{22}}{7} \times 10 \times 10 = 314.29c{m^2}$
Now for total surface area we will add the curved surface area with base area i.e. $785.71c{m^2} + 314.29c{m^2} = 1100c{m^2}$
Hence option A is the correct answer.

Note: Whenever you get this type of question the key concept of solving is first draw a neat diagram so that you can understand the question properly and have knowledge of the curved surface area required to form the cone and for total surface area we have to add the area of base also. Students generally forget to add the area of base and that will give the wrong answer.