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Question
The ratio between the radius of the base and the height of a cylinder is 2 : 3. Find the total surface area of the cylinder, if its volume is 1617 cm3.
Solution
Let r cm be the radius and h cm be the height of the cylinder. It is given that the ratio of rand h is 2:3, so h = 1.5r
The volume of the cylinder (V) is 1617 cm3.
So, we can find the radius and the height of the cylinder from the equation given below:
V= πr2h
1617 = πr2h
1617 = πr2(1.5r)
r3 =343
r = 7 cm and h = 10.5 cm
Total surface area = 2πr2+2πrh = \[2 \times \frac{22}{7} \times 7^2 + 2 \times \frac{22}{7} \times 7 \times 10 . 5 = 770 {cm}^2\]
Hence, the total surface area of the cylinder is 770 cm2.
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