Question

Question 4
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 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.

Answer 1

Dimensions of cuboid $=15cm\times 10cm\times 3.5cm$, radius of cone $=0.5$ cm, depth of cone = 1.4 cm
Volume of cuboid = length $\times$ width $\times$ height
$=15\times 10\times 3.5=525c{m}^3$
Volume of cone
$=\frac{1}{3}\pi r^{2}h$
$=\frac{1}{3}\times \frac{22}{7}\times {0.5}^2\times 1.4$
$=\frac{11}{30}c{m}^3$
Volume of wood = Volume of cuboid – 4 $\times$ Volume of cone
$=525-4\times \frac{11}{30}$
$=525-\frac{22}{15}$
$=523.53c{m}^3$