If the diameter of the base of a cone is 56 cm and its curved surface area is 3080 cm2, then what will be its volume (in cm3)? (Use π = 22/7)
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 17248.
Curved surface area of a cone = πrl
Volume of a cone = (1/3)πr2h
Where r is the radius, l is the slant height, and h is the height
Diameter = 56 cm
Radius (r) = 56/2 = 28 cm
So, (22/7) × 28 × l = 3080
⇒ l = 3080/88 = 35 cm
Height (h) = √(352 - 282) = √(1225 - 784) = √441 = 21 cm
Volume = (1/3) × (22/7) × 282 × 21 = 17248 cm3
Therefore, the volume of the cone is 17248 cm3.