# ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.5 in Chapter 17 - Mensuration

Question 2 Mensuration Exercise 17.5

The diameter of a metallic sphere is 6 cm. The sphere is melted and drawn into a wire of uniform cross-section. If the length of the wire is 36 m, find its radius.

Solution:

Even if the new shape may be different, when we change one solid shape into another, its volume stays the same.

Given diameter of the metallic sphere = 6 cm

Radius of the sphere, r = 6/2 = 3 cm

Volume of the sphere, V = (4/3)π r3

= (4/3)π x33

= 4 π x 9

= 36 π cm3

Length of the wire, h = 36 m = 3600 cm

Since the sphere is melted and drawn into a wire, volume remains the same.

Volume of the wire, π r2h = 36π

π r2×3600 = 36π

r2 = 1/100

r = 1/10 = 0.1 cm = 1 mm

Hence the radius of the wire is 1 mm.

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