Question

A conical shaped container with height $21cm$ has area of its base equal to $154c{m}^2$. Find the number of lemons (somewhat spherical in shape) that can be put in the container if each lemon has a radius of $1.4cm$.

• A.
  80
• B.
  84
• C.
  90
• D.
  94

Answer 1

The correct option is D

94
Volume of cone
$=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times 154\times 21=1078c{m}^3$

Volume of a lemons (spherical)
$=\frac{4}{3}\times \pi \times r^3=\frac{4}{3}\times \frac{22}{7}\times 1.4\times 1.4\times 1.4=11.5c{m}^3$

Volume of cone = Number of lemons $\times$ Volume of one lemons
$\Rightarrow \text{Number of lemons}=\frac{\text{Volume of the cone}}{\text{Volume of one lemons}}=\frac{1078c{m}^3}{11.5c{m}^3}=93.74\approx 94\text{lemons}$