Question

The total surface area of a cylinder is 264m². Find its volume if its height is 5 more than its radius.

Answer 1

Let r be the radius of the cylinder.
Then, Height (h) = 5 + r    ..................................(1)
Total surface area of cylinder = 264m²
(2 x π x r x h) + (2 x π x r²) = 264
2 π r (h + r) = 264
2 π r (5 + r + r) = 264        ...[From(1)]

r(5 + 2r) = `(264)/(2π)`
5r + 2r² = 42
2r² + 5r - 42 = 0
2r² + 12r - 7r - 42 = 0
2r(r + 6) - 7(r+ 6) = 0
(2r - 7)(r + 6) = 0
i.e., (2r - 7) = 0  or  (r + 6) = 0
2r = 7  or  r = -6

r = `(7)/(2)`
r = 3.5m
Since, radius of a cylinder cannot be negative, we take the value of r = 3.5m
∴ Height (h) 
= 5 + 3.5
= 8.5m
Volume
= π x r² x h

= `(22)/(7) xx 3.5^2 xx 8.5`
= 327.25m³.