Question

The sum of the radius of the base and the height of a solid cylinder is 37 m. If the total surface area of the cylinder be 1628 sq m, its volume is

(a) 4620 m³ 

(b) 4630 m³ 

(c) 4520 m³  

(d) 4830 m³ 

Answer 1

(a) 4620 m³

Given, r + h = 37 m. 

Also, total surface area = 2πr(r + h) 

∴ 2πr(r + h) = 1628 ⇒ 2πr x 37 = 1628

r = \(\frac{1628\times7}{2\times22\times37}\) = 7 m

∴ Height (h) = 37 m – 7 m = 30 m

Its volume = πr²h = \(\bigg(\frac{22}{7}\times7\times7\times30\bigg)\) = m³ = 4620 m³.