The height of a right circular cone is 63 cm and the area of its curved surface is five times the area of its base. What is the volume (in cm3) of the cone? (Use π = 22/7)
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 10914.75.
Height of the cone (h) = 63 cm
The curved surface area of cone = πrl where l is the slant height
Base Area of cone = πr2
Slant height (l) = √(r2 + h2)
Volume of cone = (1/3)πr2h
So, πrl = 5πr2
⇒ l = 5r
⇒ 5r = √(r2 + h2)
⇒ r2 + h2 = 25r2
⇒ h2 = 24r2
⇒ 24r2 = 632 = 3969
⇒ r2 = 3969/24 = 1323/8
Volume = (1/3)πr2h = (1/3) × (22/7) × (1323/8) × 63 = 261954/8 = 10914.75 cm3
Therefore, the volume of the cone is 10914.75 cm3.