Question

A toy in the shape of a hemisphere of radius 7cm is surmounted by a cone of slant height 25cm. The toy is placed in a cylindrical box of radius 70cm and height 1m, which is to be packed and dispatched. Find how many such toys can be accomodated in the box. Assume packaging occupies a volume of $\frac{11}{3}$ $c{m}^3$ for each toy and all toys needs to be packed.(Take $\pi =\frac{22}{7}$)

• A. 788

Answer 1

The correct option is A 788

Volume of the toy = volume of hemisphere + volume of cone

Height of the cone, h = $\sqrt{(25{)}^2-(7{)}^2}=24$

=$\frac{2}{3}\pi r^3+\frac{1}{3}\pi r^{2}h$

= $\frac{22}{7}\times \left(7{)}^2\right[\frac{2\times 7}{3}+8]$

= 1950.66$c{m}^3$

Volume of the box = $\pi r^2$h = $\frac{22}{7}\times (70{)}^2$100 = 1540000$c{m}^3$

Volume of the toy + packaging volume = $1950.66+\frac{11}{3}=\frac{5862.98}{3}$

Number of packaged toys that can fit into the box = $\frac{volumeofbox}{volumeofpackagedtoy}$

$=\frac{1540000}{\left(\frac{5862.98}{3}\right)}$ ≈ 788.