Question

# (a) A solid right circular copper cone of height 15 cm and radius 6 cm is melted and recast into smaller copper cones of height 3 cm and radius 2 cm. How many such smaller cones can be made? (b) Two solid spheres of radii 2 cm and 4 cm are melted and recast into a cone of height 8 cm. Find the radius of the cone so formed. [6 MARKS]

Solution

## Each Part: 2 Marks (a) Volume of the bigger cone =13×π×62×15cm^3 = 180 \pi ~cm^3 Volume of one smaller cone =13×π×22×3cm^3 = 4 \pi ~cm^3 \therefore Number of smaller cones =Volume of bigger coneVolume of a smaller cone =180π cm34π cm3=45 Hence, the number of smaller cones is 45 (b)  Radii of two solid sphere are 2 cm and 4 cm. Spheres are melted and recast into a cone of height 8 cm ⇒ Vol. of two spheres = Vol. of one cone ⇒43πr31+43πr32=13πR2H ⇒43π[r31+r32]=13πR2×8 ⇒4[23+43]=8R2 ⇒4×72=8R2 ⇒R2=36 cm ⇒R=6 cm Radius of cone = 6 cm    Mathematics

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