F.3 mensuration

1. When a metal is heated, the length of the rod increases by 8%. Find the percentage increase in the volume of the metal rod.

(Original length) : (New length)
= 1 : (1 + 8%)

(Original volume) : (New volume)
= 1³ : (1 + 8%)³
= 1 : 1.259712

Percentage increase
= [(1.259712 - 1)/1] x 100%
= 25.9712%


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2. A right circular metal cone with the height of 16 cm and the base radius of 4 cm is melted and recast into a solid sphere. What is the radius of the sphere
Let r cm be the radius of the sphere.

(4/3)πr³ = (1/3)π(4)²(16)
r³ = 64
r = 4

Radius of the sphere = 4 cm