Question

Slant height and radius of a cone is 42m and 21m respectively then Calculate the total surface area and curved surface area.​

Answer 1

$\large{\red{\bold{\underline{Given:}}}}$

$\sf \: (i) \: Slant \: height \: of \: the \: cone (l) = 42m \\ \\ \sf \: (ii) \: Radius \: of \: its \: base(r) = 21m$

$\large{\green{\bold{\underline{To \: Find:}}}}$

$\sf \: (i) \: Total \: surface \: area \: of \: cone \\ \\ \sf \: (ii) \: Curved \: surface \: area \: of \: cone$

$\large{\blue{\bold{\underline{Formula \: Used:}}}}$

$\sf \: Total \: surface \: area = \pi rl + \pi {r}^{2} \\ \\ \sf \: Curved \: surface \: area = \pi rl$

$\large{\red{\bold{\underline{Solution:}}}}$

$\sf \: Let's \: consider \: total \: surface \: area \: as \: T.S.A. \\ \sf \: And \: curved \: surface \: area \: as \: C.S.A.$

$\large{\pink{\bold{\underline{Then:}}}}$

$\sf \: \longrightarrow \: T.S.A = \pi r(r + l) \\ \\ \longrightarrow \: \sf \: T.S.A = \frac{22}{7} \times 21(21 + 42) \\ \\ \longrightarrow \: \sf \: T.S.A = \frac{22}{7} \times 21(63) \\ \\ \longrightarrow \: \sf \: T.S.A = \frac{22}{\cancel7} \times \cancel21 (63) \\ \\ \longrightarrow \: \sf \:T.S.A = 22 \times 3 \times 63 \\ \\ \longrightarrow \: \sf \:T.S.A = 4158 \: {m}^{2}$

$\large{\green{\bold{\underline{And:}}}}$

$\sf \longrightarrow \: \sf \: C.S.A = \pi rl \\ \\ \longrightarrow \: \sf \: C.S.A = \frac{22}{7} \times 21 \times 42 \\ \\ \longrightarrow \: \sf \: C.S.A = \frac{22}{\cancel7} \times \cancel21 \times 42 \\ \\ \longrightarrow \: \sf \: C.S.A = 22 \times 3 \times 42 \\ \\ \longrightarrow \: \sf \: C.S.A = 2772 \: {m}^{2}$

$\large{\red{\bold{\underline{Therefore:}}}}$

$\sf \: Total \: surface \: area \: of \: cone \: is \: 4158 {m}^{2} \: and \\ \sf \: curved \: surface \: area \: of \: cone \: is \: 2772 {m}^{2}.$