the radius & height of a right circular cone are in ratio 4:3 & its volume is 2156 cu. cm. Find the curved surface area and the total surface area of the cone
Answers
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
___________________________
➳ TSA of cone = πr² + πrl
➳ TSA of cone = 22/7 × 14² + 770
➳ TSA of cone = 616 + 770
➳ TSA of cone = 1386 cm²