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ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.1 in Chapter 17 - Mensuration
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The ratio between the curved surface and the total surface of a cylinder is 1 : 2.
Find the volume of the cylinder, given that its total surface area is 616 cm2.
Solution:
The area of the cylinder is determined by adding the areas of its two circular bases and curving surface.
Given the ratio of curved surface area and the total surface area = 1:2
Total surface area = 616 cm2
Curved surface area = 616/2 = 308 cm2
2π rh = 308
rh = 308/2π
= 308×7/2×22
rh = 49 …(i)
Total surface area, 2π rh+2π r2 = 616
308+2π r2 = 616
2π r2 = 616-308
2π r2 = 308
π r2 = 308/2 = 154
r2 = 154/π = 154×7/22 = 49
Taking square root on both sides
r = 7
Substitute r in (i)
rh = 49
7×h = 49
h = 49/7 = 7 cm
Volume of the cylinder, V =π r2h
= (22/7)×72×7
= 1078 cm3
Hence the volume of the cylinder is 1078 cm3.
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