Question

A conical shaped container with a height of 30 cm has the area of its base equal to 100 $c{m}^2$. Find the number of grapes (spherical in shape) that can be put in the container if each grape has a radius of 0.42 cm.

• A. 302
• B. 312
• C. 322
• D. 332

Answer 1

The correct option is C

322

Volume of cone $=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times 100\times 30=1000c{m}^3$
Volume of a grape (spherical) $=\frac{4}{3}\times \pi \times r^3=\frac{4}{3}\times \frac{22}{7}\times 0.42\times 0.42\times 0.42=0.31c{m}^3$
Number of grapes $\times$ Volume of one grape = Volume of cone
Number of grapes $=\frac{Volumeofthecone}{Volumeofonegrape}=\frac{1000c{m}^3}{0.31c{m}^3}$ =3225.8 $\approx$ 3225 grapes.