Question

Calculate the total surface area and curved surface area of cone of slant height 21 m and radius is 7m.​

Answer 1

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

$\sf \: (i) \: Slant \: height \: of \: the \: cone (l) = 21 m \\ \\ \sf \: (ii) \: Radius \: of \: its \: base(r) = 7m$

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

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

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

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

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

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

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

$\sf \: \longrightarrow \: T.S.A = \pi r(r + l) \\ \\ \longrightarrow \: \sf \: T.S.A = \frac{22}{7} \times 7(7 + 21) \\ \\ \longrightarrow \: \sf \: T.S.A = \frac{22}{7} \times 7(28) \\ \\ \longrightarrow \: \sf \: T.S.A = \frac{22}{\cancel7} \times \cancel7(28) \\ \\ \longrightarrow \: \sf \:T.S.A = 22 \times 28 \\ \\ \longrightarrow \: \sf \:T.S.A = 616 \: {m}^{2}$

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

$\sf \longrightarrow \: \sf \: C.S.A = \pi rl \\ \\ \longrightarrow \: \sf \: C.S.A = \frac{22}{7} \times 7 \times 21 \\ \\ \longrightarrow \: \sf \: C.S.A = \frac{22}{\cancel7} \times \cancel7 \times 21 \\ \\ \longrightarrow \: \sf \: C.S.A = 22 \times 21\\ \\ \longrightarrow \: \sf \: C.S.A = 462 \: {m}^{2}$

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

$\sf \: Total \: surface \: area \: of \: cone \: is \: 616 {m}^{2} \: and \\ \sf \: curved \: surface \: area \: of \: cone \: is \: 462 {m}^{2}.$

Answer 2

Answer:

TSA = πr(r+l)

= 22/7× 7 {7+21}

= 22× 28

= 616m^2

CSA = 2πrl

= 2× 22/7 ×7 ×21

= 44× 21

= 924m^2