# The radius and slant height of a cone are 7 cm and 10 cm respectively. Find its curved surface area. ($\pi = \dfrac{{22}}{7}$ )

Last updated date: 18th Mar 2023

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Answer

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Hint: Here, we will be proceeding by drawing a diagram using the given data (radius and slant height of the cone) and determine the curved surface area of this cone with the help of formula for the curved surface area of the cone i.e., ${\text{C}}{\text{.S}}{\text{.A}} = \pi rl$.

Complete step-by-step answer:

Given, Radius of the cone r = 7 cm

Slant height of the cone l = 10 cm

As we know that the formula for the curved surface area of the cone with radius r and slant height l is given by

${\text{C}}{\text{.S}}{\text{.A}} = \pi rl$

Using the above formula, the curved surface area of the given cone is given by

${\text{C}}{\text{.S}}{\text{.A}} = \pi rl = \dfrac{{22}}{7} \times 7 \times 10 = 220{\text{ c}}{{\text{m}}^2}$

Hence, the curved surface area of the cone with a radius of 7 cm and slant height of 10 cm respectively is 220 sq. cm.

Note: In any cone with radius r and height h, the slant height h is given by $l = \sqrt {{r^2} + {h^2}} $. For calculation of curved surface area of the cone (${\text{C}}{\text{.S}}{\text{.A}} = \pi rl$), radius and slant height of the cone is required. But if instead of slant height l, height of the cone h is given then we will be using formula $l = \sqrt {{r^2} + {h^2}} $ to find the value of slant height first.

Complete step-by-step answer:

Given, Radius of the cone r = 7 cm

Slant height of the cone l = 10 cm

As we know that the formula for the curved surface area of the cone with radius r and slant height l is given by

${\text{C}}{\text{.S}}{\text{.A}} = \pi rl$

Using the above formula, the curved surface area of the given cone is given by

${\text{C}}{\text{.S}}{\text{.A}} = \pi rl = \dfrac{{22}}{7} \times 7 \times 10 = 220{\text{ c}}{{\text{m}}^2}$

Hence, the curved surface area of the cone with a radius of 7 cm and slant height of 10 cm respectively is 220 sq. cm.

Note: In any cone with radius r and height h, the slant height h is given by $l = \sqrt {{r^2} + {h^2}} $. For calculation of curved surface area of the cone (${\text{C}}{\text{.S}}{\text{.A}} = \pi rl$), radius and slant height of the cone is required. But if instead of slant height l, height of the cone h is given then we will be using formula $l = \sqrt {{r^2} + {h^2}} $ to find the value of slant height first.

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