Name: Parts of a Cuboid
Uploaded: 2019-07-19
Duration: 5 min 14 s
Description: Take this quick lesson on learning everything you'll need to know about cuboids and their faces, edges and vertices. Check out this short video!

Question

A pen stand made of wood is in the shape of a cuboid with four conical depressions and a cubical depression to hold the pens and pins, respectively. The dimensions of cuboid are

10 cm, 5 cm and 4 cm

. The radius of each of the conical depressions is

3 cm

. Find the volume of the wood in the entire stand.

Accepted Answer

Given that, length of cuboid pen stand $(l) = 10 cm$

Breadth of cubiod per stand $(b) = 5 cm$

and height of cuboid pen stand $(h) = 4 cm$

$∴$ Volume of cuboid pen stand $= l \times b \times h = 10 \times 5 \times 4 = 200 {cm}^{3}$

Also, radius of conical depression $(r) = 0.5 cm$

and height (depth) of a conical depression $(h_{1}) = 2.1 cm$

$∴$ Volume of a conical depression $= \frac{1}{3} {πr}^{2} h_{1}$

$= \frac{1}{3} \times \frac{22}{7} \times 0.5 \times 0.5 \times 2.1$

$= \frac{22 \times 5 \times 5}{1000} = \frac{22}{40} = \frac{11}{20} = 0.55 {cm}^{3}$

Also, given

Edge of cubical depression $(a) = 3 cm$

$∴$ Volume of cubical depression $= (a) = {(3)}^{3} = 27 {cm}^{3}$

So, volume of $4$ conical depressions

$= 4 \times$ volume of conical depression

$= 4 \times \frac{11}{20} = \frac{11}{5} {cm}^{3}$

Hence, the volume of wood in the entire pen stand $=$ volume of cuboid pen stand $-$ volume of $4$ conical depressions $-$ volume of a cubical depressions

$= 200 - \frac{11}{5} - 27 = 200 - \frac{146}{5}$

$= 200 - 29.2 = 170.8 {cm}^{3}$

So, the required volume of the wood in the entire stand is $170.8 {cm}^{3}$ .

Important Questions on Surface Areas and Volumes

Learn and Prepare for any exam you want !

A pen stand made of wood is in the shape of a cuboid with four conical depressions and a cubical depression to hold the pens and pins, respectively. The dimensions of cuboid are 10cm, 5cm and 4cm. The radius of each of the conical depressions is 3cm. Find the volume of the wood in the entire stand.

Important Questions on Surface Areas and Volumes

Learn and Prepare for any exam you want !