# ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.1 in Chapter 17 - Mensuration

Question 20 Mensuration Exercise 17.1

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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