Question

The radius and height of a right circular cone are in the ratio 4 : 3 and its volume is 2156 cu. Cm. Find the curved surface area and the total surface area of the cone.

Answer 1

Answer :-

We have ratio of radius and cone is 4:3 and volume of cone = 2156 cubic cm.

We know that volume of cone :-

$= \frac{1}{ 3 }\pi {r}^{2} h$

We have ratio of radius and height is 4:3

$2156 = \frac{1}{3} \times \frac{22}{7} \times {(4x)}^{2} \times 3x \\ \\ \frac{2156 \times 3 \times 7}{22} = {16x}^{2} + 3x \\ \\ \frac{2058}{16 \times 3} = {x}^{2} + x \\ \\ 42.875 = {x}^{2} + x$

Answer 2

Answer:

Let the radius be 4x and height be 3x of the right circular cone.

We have,

Area of the right circular cone = 2156 cm³

★ According to Question now,

➨ Volume of cone = ⅓ πr²h

➳ 2156 = 1/3 × 22/7 × (4x)² × (3x)

➳ 2156 = 1/3 × 22/7 × 16x² × 3x

➳ 2156 = 22/7 × 16x² × x

➳ 16x³ = 2156 × 7/22

➳ x³ = 98 × 7/16

➳ x³ = 7 × 7 × 7/2 × 2 × 2

➳ x = 7/2

➳ x = 3.5 cm

Therefore,

Radius = 4x = 4(3.5) = 14 cm

Height = 3x = 3(3.5) = 10.5 cm

______________________

➳ Slant height (l)² = r² + h²

➳ l² = (14)² + (3.5)²

➳ l² = 196 + 110.25

➳ l² = 306.25

➳ l = √306.25

➳ Slant Height (l) = 17.5 cm

_____________________

➳ CSA of cone = πrl

➳ CSA of cone = 22/7 × 14 × 10.5

➳ CSA of cone = 22 × 2 × 10.5

➳ CSA of cone = 44 × 10.5

➳ CSA of cone = 770 cm²