The volume of a right circular cone is 9856 cm3. If the diameter of the base is 28 cm, find :
(i) height of the cone
(ii) slant height of the cone
(iii) curved surface area of the cone.
Answers
Given : Volume of a right circular cone = 9856 cm³
The diameter of the base = 28 cm
Radius , r = 28/2 = 14 cm
Volume of a right circular cone = ⅓πr²h
9856 = ⅓ × 22/7 × 14 × 14 × h
9856 × 3 = 22 × 2 × 14 × h
h = (9856 × 3)/(22 × 2 × 14)
h = (448 × 3)/(28)
h = 16 × 3
height of the cone, h = 48 cm
Slant height , l = √ r² + h²
l = √14² + 48²
l = √(196 + 2304)
l = √2500
Slant height ,l = 50
Curved surface area of cone , C.S A = πrl
C.S A = 22/7 × 14 × 50
Curved surface area of cone = 2200 cm²
Hence, the Height of the cone is 48 cm, Slant height is 50 cm and C.S.A of Cone is 2200 cm².
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Answer:
Step-by-step explanation:
Volume of a right circular cone = ⅓πr²h
9856 = ⅓ × 22/7 × 14 × 14 × h
9856 × 3 = 22 × 2 × 14 × h
h = (9856 × 3)/(22 × 2 × 14)
h = (448 × 3)/(28)
h = 16 × 3
height of the cone, h = 48 cm
Slant height , l = √ r² + h²
l = √14² + 48²
l = √(196 + 2304)
l = √2500
Slant height ,l = 50
Curved surface area of cone , C.S A = πrl
C.S A = 22/7 × 14 × 50
Curved surface area of cone = 2200 cm²