Question

Calculate the total surface area and curved surface area of cone if slant height of that is 56 m and radius is 49m.​

Answer 1

Answer:

We know that formula of the curved surface area of a cone is πrl, where r is the base radius and l is the slant height of the cone.

Here, given the base radius, r=5.6cm

slant height, l=9cm

∴ Curved surface area of the cone= πrl

=

7

22

×5.6×9

=

7

1108.8

=158.8cm

2

.

Answer 2

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

$\sf \: (i) \: Slant \: height \: of \: the \: cone (l) = 56m \\ \\ \sf \: (ii) \: Radius \: of \: its \: base(r) = 49m$

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

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

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

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

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

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

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

$\sf \: \longrightarrow \: T.S.A = \pi r(r + l) \\ \\ \longrightarrow \: \sf \: T.S.A = \frac{22}{7} \times 49(49 + 56) \\ \\ \longrightarrow \: \sf \: T.S.A = \frac{22}{7} \times 49(105) \\ \\ \longrightarrow \: \sf \: T.S.A = \frac{22}{\cancel7} \times \cancel49 (105) \\ \\ \longrightarrow \: \sf \:T.S.A = 22 \times 7 \times 105 \\ \\ \longrightarrow \: \sf \:T.S.A = 16170 \: {m}^{2}$

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

$\sf \longrightarrow \: \sf \: C.S.A = \pi rl \\ \\ \longrightarrow \: \sf \: C.S.A = \frac{22}{7} \times 49 \times 56 \\ \\ \longrightarrow \: \sf \: C.S.A = \frac{22}{\cancel7} \times \cancel49 \times 56 \\ \\ \longrightarrow \: \sf \: C.S.A = 22 \times 7 \times 56 \\ \\ \longrightarrow \: \sf \: C.S.A = 8624 \: {m}^{2}$

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

$\sf \: Total \: surface \: area \: of \: cone \: is \: 16170 {m}^{2} \: and \\ \sf \: curved \: surface \: area \: of \: cone \: is \: 8624 {m}^{2}.$