Question

A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are $15cm\times$$10cm\times$$3.5cm.$ The diameter of each of the depressions $1cm$ and the depth is $1.4cm.$ Find the volume of the wood in the entire stand.

Answer 1

It is given that the dimensions of the cuboidal part are $15cm\times$ $10cm\times$ $3.5cm$.

volume of the cuboid $=(15\times 10\times 3.5){cm}^3=525{cm}^3$

It is given that there are four conical depressions such that the radius of each depression is $0.5cm$ and the depth is $1.4cm$

Volume of wood taken out to make four cavities $=4\times$ volume of a cone of base radius $0.5cm$ and height $1.4cm$

$=4\times \frac{1}{3}\pi r^{2}h$

$=4\times \frac{1}{3}\times \frac{22}{7}\times 0.5\times 0.5\times 1.4{cm}^3$

$=\frac{22}{15}{cm}^3=1.47{cm}^3$ (approximately)

Hence volume of the wood in the entire stand $=(525-1.47){cm}^3=523.53{cm}^3$