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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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