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

Question 8 Mensuration Exercise 17.5

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.



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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