Question

Given that slant height and radius of a cone both is 7cm then
find out
total surface area of the cone
also curved surface area of the cone​

Answer 1

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

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

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

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

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

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

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

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

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

$\sf \: \longrightarrow \: T.S.A = \pi r(r + l) \\ \\ \longrightarrow \: \sf \: T.S.A = \frac{22}{7} \times 7(7 + 7) \\ \\ \longrightarrow \: \sf \: T.S.A = \frac{22}{7} \times 7(14) \\ \\ \longrightarrow \: \sf \: T.S.A = \frac{22}{\cancel7} \times \cancel7(14) \\ \\ \longrightarrow \: \sf \:T.S.A = 22 \times 14 \\ \\ \longrightarrow \: \sf \:T.S.A = 308 \: {m}^{2}$

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

$\sf \longrightarrow \: \sf \: C.S.A = \pi rl \\ \\ \longrightarrow \: \sf \: C.S.A = \frac{22}{7} \times 7 \times 7 \\ \\ \longrightarrow \: \sf \: C.S.A = \frac{22}{\cancel7} \times \cancel7 \times 7 \\ \\ \longrightarrow \: \sf \: C.S.A = 22 \times 7 \\ \\ \longrightarrow \: \sf \: C.S.A = 154 \: {m}^{2}$

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

$\sf \: Total \: surface \: area \: of \: cone \: is \: 308 {m}^{2} \: and \\ \sf \: curved \: surface \: area \: of \: cone \: is \: 154 {m}^{2}.$

Answer 2

Answer:

Given:

Slant height, l = 10 cm

Base radius of cone, r = 7 cm

To find out:

Find the Curved surface area of a right circular cone?

Formula used:

Curved surface area = πrl

Solution:

Curved surface area = πrl

= 22/7 × 7 × 10

= 22 × 10

= 220 cm²

Hence, the Curved surface area of given cone is 220 cm².

Additional information:

Total surface area of cone = π × r ( l + r )

volume of cone = 1/3 × π × r² × h

Surface area of sphere = 4 × π × r²

Volume of sphere = 4/3 × π × r³

Explanation: