Question

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

• A. 3020
• B. 312
• C. 322
• D. 3225

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)
$=\frac{4}{3}\times \pi \times r^3=\frac{4}{3}\times \frac{22}{7}\times 0.42\times 0.42\times 0.42=0.31c{m}^3$

Volume of cone = Number of grapes $\times$ Volume of one grape
$\Rightarrow \text{Number of grapes}=\frac{\text{Volume of the cone}}{\text{Volume of one grape}}=\frac{1000c{m}^3}{3.10c{m}^3}=322.58\approx 322\text{grapes}$