Question

Find the total surface area and curved surface area of a cone of slant height 42 m and radius is 35m.​

Answer 1

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

$\sf \: (i) \: Slant \: height \: of \: the \: cone (l) = 42m \\ \\ \sf \: (ii) \: Radius \: of \: its \: base(r) = 35m$

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

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

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

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

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

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

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

$\sf \: \longrightarrow \: T.S.A = \pi r(r + l) \\ \\ \longrightarrow \: \sf \: T.S.A = \frac{22}{7} \times 35(42 + 35) \\ \\ \longrightarrow \: \sf \: T.S.A = \frac{22}{7} \times 35(77) \\ \\ \longrightarrow \: \sf \: T.S.A = \frac{22}{\cancel7} \times \cancel35 (77) \\ \\ \longrightarrow \: \sf \:T.S.A = 22 \times 5 \times 77 \\ \\ \longrightarrow \: \sf \:T.S.A = 8470 \: {m}^{2}$

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

$\sf \longrightarrow \: \sf \: C.S.A = \pi rl \\ \\ \longrightarrow \: \sf \: C.S.A = \frac{22}{7} \times 35 \times 42 \\ \\ \longrightarrow \: \sf \: C.S.A = \frac{22}{\cancel7} \times \cancel35 \times 42 \\ \\ \longrightarrow \: \sf \: C.S.A = 22 \times 5 \times 42 \\ \\ \longrightarrow \: \sf \: C.S.A = 4620 \: {m}^{2}$

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

$\sf \: Total \: surface \: area \: of \: cone \: is \: 8470 {m}^{2} \: and \\ \sf \: curved \: surface \: area \: of \: cone \: is \: 4620 {m}^{2}.$

Answer 2

Hey Mate !

• Slant Height (l) = 42 m
• Radius (R) = 35 m

Total Surface Area = πr(r + l)

⇒T.S.A = 22/7 * 35(42 + 35)

⇒T.S.A = 22/7 * 35 (77)

⇒T.S.A = 22 * 35 * 11

⇒T.S.A = 8470

Total Surface Area is 8470 m²

_________________________

Curved Surface Area = πrl

⇒C.S.A = 22/7 * 35 * 42

⇒C.S.A = 22 * 5 * 42

⇒C.S.A = 4620

Curved Surface Area is 4620 m²