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 $15cm$ by $10cm$ by $3.5cm$. The radius of each of the depressions is $0.5cm$ and the depth is $1.4cm$. Find the volume of wood in the entire stand (see Fig.).

Answer 1

Given : Length of cuboid $\left(l\right)=15cm$

Breadth of cuboid $\left(b\right)=10cm$

Height of cuboid $\left(h\right)=3.5cm$

Radius of the conical part $\left(r\right)=0.5cm$

Height of the conical part $\left(H\right)=1.4cm$

$TotalVolumewoodintheentires\tan d=VolumeofCuboid–Volumeoffourconicalpart$

$=(l\times b\times h)–4\times \left(\frac{1}{3}\pi r^{2}H\right)$

$=(15\times 10\times 3.5)–4\times \frac{1}{3}\times \frac{22}{7}\times {\left(0.5\right)}^2\times 1.4$

$=\left(15\times 10\times \frac{35}{10}\right)–4\left(\frac{1}{3}\times \frac{22}{7}\times 0.5\times 0.5\times 1.4\right)$

$=\left(15\times 35\right)–4\times \frac{1}{3}\times \frac{22}{7}\times \frac{1}{2}\times \frac{1}{2}\times \frac{14}{10}$

$=525–\frac{1}{3}\times 22\times \frac{1}{5}$

$=525–\frac{22}{15}$

$=525–1.466$

$=523.53c{m}^3$

Therefore, the volume of wood is$523.53c{m}^3$