Q) A metallic solid sphere of radius 10.5 cm melted and recasted into smaller solid cones each of radius 3.5 cm and height 3 cm. How may cones will be made?

Ans:

Step 1: Let’s draw a diagram to better understand the question:

Here, according to question, we have sphere of radius 10.5 cm.

This sphere is melted to make cones of radius 3.5 cm and height 3 cm.

Step 2: We know the volume of a sphere, V_S = () π r³

∴ V_S = () π (10.5)³

∴ V_S = 4 x π x 10.5 x 10.5 x 3.5

Step 3: We know the volume of a cone, V_C = () π r² h

∴ V_C = () π (3.5)² (3)

∴ V_C = π x 3.5 x 3.5

Step 4: Now this sphere of V_S  is melted to make cones of V_C each.

By unitary method, we can say that:

∴ V_C volume is for = 1 cone

∴ V_S volume will make = cones

=

= 4 x 3 x 3 x 3.5 = 126 cones

Therefore, the sphere will make 126 cones of given dimensions.

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