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A toy is a cone mounted on a hemisphere, both of radius r. If the cone height equals r, the total volume is:

Class 10Volume of Combined SolidsMensuration

A $p i r^{3}$
B $\frac{2}{3} p i r^{3}$
C $\frac{1}{3} p i r^{3}$
D $\frac{4}{3} p i r^{3}$

Step-by-Step Solution

Cone =

\frac{1}{3}

π

r^{2} (r) = \frac{1}{3}

π

r^{3}

; hemisphere =

\frac{2}{3}

π

r^{3}

. Sum =

(\frac{1}{3} + \frac{2}{3})

π

r^{3}

= π

r^{3}

.

Answer: A)

p i r^{3}

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