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

Two spheres of the same metal weigh 1 kg and 7 kg. The radius of the smaller sphere is 3 cm. The two spheres are melted to form a single big sphere. Find the diameter of the big sphere.

Solution:

When we convert one solid shape to another, its volume remains the same, no matter how different the new shape is.

For same material, density will be same.

Density = mass/Volume

Mass of the smaller sphere, m1 = 1 kg

Mass of the bigger sphere, m2 = 7 kg

The spheres are melted to form a new sphere.

So the mass of new sphere, m3 = 1+7 = 8 kg

Density of smaller sphere = density of new sphere

Let V1 be volume of smaller sphere and V3 be volume of bigger sphere.

m1/V1 = m3/V3

1/V1 = 8/V3

V1/ V3 = 1/8 …(i)

Given radius of the smaller sphere, r = 3 cm

V1 = (4/3)π r3

V1 = (4/3) π 33

V1 = 36π

Let R be radius of new sphere.

V3 = (4/3)π R3

V1/ V3 = 36π ÷(4/3)π R3

V1/ V3 = 27/R3 …(ii)

From (i) and (ii)

1/8 = 27/R3

R3 = 27×8 = 216

Taking cube root on both sides,

R = 6 cm

So diameter of the new sphere = 2R = 2×6 = 12 cm

Hence diameter of the new sphere is 12 cm.

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