The radii of the ends of a frustum of a right circular cone are 5 metres and 8 metres and its lateral height is 5 metres. Find the lateral surface and volume of the frustum.
Answers
Answer:
The Lateral surface area of the frustum of the cone is 204.28 cm² and Volume of the frustum is 540.57 cm³.
Step-by-step explanation:
SOLUTION :
Given :
Lateral(Slant) height of frustum of a cone, l = 5 cm
Radius of bottom of Frustum of a cone, R = 8 cm
Radius of top of Frustum of a cone, r = 5 cm
Lateral surface area of the frustum of the cone = πl (R + r)
= 22/7 × 5 (8 + 5)
= 110/7 × 13
= 1430/7 = 204.28
Lateral surface area of the frustum of the cone = 204.28 cm²
Height of the cone,h = √l² - (R - r)²
h = √5² - (8 - 5)²
h = √25 - 3² = √25 - 9 = √16 = 4
Height of the cone,h = 4 cm
Volume of the frustum = ⅓ πh(R² + r² + Rr)
= ⅓ × π × 4 (8² + 5² + 8 × 5)
= ⅓ × π × 4 (64 + 25 + 40)
= 4π/3 × 129
= 4 × 22/7 × ⅓ × 129
= 11352 / 21 = 540.57
Volume of the frustum = 540.57 cm³
Hence, the Lateral surface area of the frustum of the cone is 204.28 cm² and Volume of the frustum is 540.57 cm³.
HOPE THIS ANSWER WILL HELP YOU….
The Lateral surface area of the frustum of the cone is 204.28 cm² and Volume of the frustum is 540.57 cm³.
Step-by-step explanation:
SOLUTION :
Given :
Lateral(Slant) height of frustum of a cone, l = 5 cm
Radius of bottom of Frustum of a cone, R = 8 cm
Radius of top of Frustum of a cone, r = 5 cm
Lateral surface area of the frustum of the cone = πl (R + r)
= 22/7 × 5 (8 + 5)
= 110/7 × 13
= 1430/7 = 204.28
Lateral surface area of the frustum of the cone = 204.28 cm²
Height of the cone,h = √l² - (R - r)²
h = √5² - (8 - 5)²
h = √25 - 3² = √25 - 9 = √16 = 4
Height of the cone,h = 4 cm
Volume of the frustum = ⅓ πh(R² + r² + Rr)
= ⅓ × π × 4 (8² + 5² + 8 × 5)
= ⅓ × π × 4 (64 + 25 + 40)
= 4π/3 × 129
= 4 × 22/7 × ⅓ × 129
= 11352 / 21 = 540.57
Volume of the frustum = 540.57 cm³
Hence, the Lateral surface area of the frustum of the cone is 204.28 cm² and Volume of the frustum is 540.57 cm³.
HOPE THIS ANSWER WILL HELP YOU….