The Ratio between Curved surface area and Total Surface area of a cylinder is 7 : 11. If Curved surface area is 704 cm2 then find the volume of the cylinder.
1. 2434 cm3
2. 2832 cm3
3. 2816 cm3
4. 2756 cm3
1. 2434 cm3
2. 2832 cm3
3. 2816 cm3
4. 2756 cm3
Correct Answer – Option 3 : 2816 cm3
Given:
Ratio of Curved surface and total surface area of cylinder = 7 : 11
Curved surface area of cylinder = 704 cm2
Formula Used:
Curved surface area = 2πrh , where r = radius of base and h = height of cylinder
Total Surface area = 2πrh + 2πr2 = 2πr(h + r)
Volume of cylinder = πr2h
Calculation:
(2πrh)/[2πr(h + r)] = 7/11
⇒ h/(h + r) = 7/11
⇒ 11h = 7h + 7r
⇒ 4h = 7r
⇒ h/r = 7/4
Let the height be 7x and radius be 4x, then,
704 = 2 × (22/7) × 7x × 4x
⇒ x2 = (704 × 7)/(28 × 22 × 2)
⇒ x2 = 4
⇒ x = 2
Putting values back in 7x and 4x we get,
Radius = 4x = 4 × 2 = 8 cm
Height = 7x = 7 × 2 = 14 cm
Volume of cylinder = (22/7) × 8 × 8 × 14
⇒ V = 2816 cm3
∴ The volume of cylinder is 2816 cm3.