Question

Curved surface area of a cone is 308cm² and it's slant height is 14cm find.
a. Radius of the base
b. Total surface area of the cone

Answer 1

EXPLANATION.

Curved surface area of a cone = 308 cm².

Slant height of a cone = 14 cm.

As we know that,

Formula of :

Curved surface area of cone = πrl.

Total surface area of cone = πr(l + r).

Using this formula in the equation, we get.

Curved surface area of cone = πrl.

⇒ 22/7 x r x 14 = 308.

⇒ 22 x r x 2 = 308.

⇒ 22 x r = 154.

⇒ r = 7 cm.

Radius of the base of cone = 7 cm.

Total surface area of cone = πr(l + r).

⇒ 22/7 x 7 (14 + 7).

⇒ 22 x (21).

⇒ 462 cm².

Total surface area of the cone = 462 cm².

MORE INFORMATION.

(1) Volume of cuboid = L x B x H.

(2) Volume of cube = a³.

(3) Volume of cylinder = πr²h.

(4) Volume of cone = 1/3πr²h.

(5) Volume of hemisphere = 2/3πr³.

(6) Volume of sphere = 4/3πr³.

Answer 2

$\color{red} \large \bold{Given,} \\ \\ \sf \: Curved \: surface \: area \: = \: 308 \: {cm}^{2} \: \: \: | \: \: \:Slant \: height \: = \: 14 \: cm \\ \\ \boxed{\sf \: Curved \: surface \: area_{(cone)} \: = \: \pi \: r \: l} \\ \\ \sf \: 308 \: = \: \frac{22}{ \cancel7} \times r \times \cancel{14} \: \: ^2 \\ \\ \sf \: 308 \: = \: 44r \\ \\ \sf \: r \: = \: \frac{308}{44} \\ \\ \sf \color{magenta}Radius \: = \: 7 \: cm \: \\ \\ \sf \: Total \: surface \: area_{(cone)} \: = \: \pi \: r \: ( \: l \: + \: r) \\ \\ \sf \: Total \: surface \: area \: = \: \frac{22}{ \cancel 7} \: \times \: \cancel 7 \: (14 \: + \: 7) \\ \\ \sf \: Total \: surface \: area \: = \:22 \: \times \: 21 \\ \\ \sf \: \color{aqua} Total \: surface \: area\: = \:462 \: {cm}^{2}$

$\color{lime}\rule{200000000 pt}{2pt}$

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²