Question
Download Solution PDFIf the area of the base of a cone is 154 cm2 and the area of the curved surface is 550 cm2, then its volume is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
Area of base of cone = 154 cm2
Area of curved surface = 550 cm2
Formula used
Volume of cone = (1/3)πr2h
Curved surface area of cone = πrl
where l is slant height
l = √h2 + r2
Calculation
Area of base of cone = πr2
(22/7) × r2 = 154
⇒ r2 = (154 × 7)/22
⇒ r2 = 1078/22
⇒ r2 = 49
⇒ r = 7 cm
Curved surface area of cone = πrl
550 = (22/7) × 7 × l
⇒ 550/22 = l
⇒ 25 = l
Volume of cone = (1/3)πr2h
h = √l2 - r2
⇒ h = √(25)2 - (7)2
⇒ h = √625 - 49
⇒ h = √576
⇒ h = 24
Volume of cone = (1/3) × (22/7) × 7 × 7 × 24
⇒ 22 × 7 × 8
⇒ 22 × 56
⇒ 1232 cm3
∴ Volume of cone is 1232 cm3
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