The height of a right circular cylinder is 10.5 m. Three times the sum of the areas of its two circular faces is twice the area of the curved surface. Find the volume of the cylinder.
Given: 3× sum of areas of two circular faces =2× area of curved surface
Height of a right circular cylinder =10.5 m
Let r be that radius of the given right circular cylinder.
3× sum of areas of two circular faces =2× area of curved surface
⇒3×2πr2=2×2πrh [∵ Area of circular face =πr2 and area of curved surface =2πrh ]
⇒6πr2=4πrh
⇒3r=2h
⇒3r=2×10.5=21
∴r=213=7 m
Now Volume of cylinder =πr2h=227×7×7×10.5 m3
=1617 m3