Name: Area of Segment
Uploaded: 2019-07-19
Duration: 7 min 50 s
Description: Do you know the result for the area of a segment? Well, this video talks about the derivation of it. So, let's dive in and master the concept in just a few m...

Question

A godown is formed of a cuboid of dimensions

63 m \times 28 m \times 5 m

covered by a half cylindrical roof. If the length and breadth of the cuboid are

63 m and 28 m

respectively, find the volume of air inside the godown. Also find the cost of roofing at the rate of

₹ 500 per square metre

.

Accepted Answer

Given, A godown is formed of a cuboid covered by a half cylindrical roof.

So, length breadth and height of cuboid are $63 m, 28 m and 5 m$ , respectively.

Length of cuboid is equals to height of cylindrical roof and breadth of cuboid is equals to diameter of cylindrical roof.

So, height of cylindrical roof $= 63 m$

And its diameter $= 28 m$

So, its radius $= \frac{1}{2} \times 28 m = 14 m$

Now, to find the volume of air inside the godown, we need to find volume of godown.

So, volume of godown $=$ Volume of cuboid $+ \frac{1}{2} \times$ Volume of cylinder

$= length \times breadth \times height + \frac{1}{2} \times {πr}^{2} h$

$= 63 \times 28 \times 5 + \frac{1}{2} \times \frac{22}{7} \times 14^{2} \times 63$

$= 8820 m^{3} + 19404 m^{3}$

$= 28224 m^{3}$

Now, surface area of cylindrical roof $= \frac{1}{2} \times 2 πrh$

$= \frac{22}{7} \times 14 \times 63$

$= 2772 m^{2}$

Now, the cost of roofing $per square metre = ₹ 500$

So, the cost of roofing $2772 m^{2}$ roof $= ₹ 500 \times 2772 = ₹ 1386000$

Hence, the volume of air inside the godown is $28224 m^{3}$ And the cost of roofing is $₹ 1386000$ .

A godown is formed of a cuboid of dimensions $63 m \times 28 m \times 5 m$ covered by a half cylindrical roof. If the length and breadth of the cuboid are $63 m and 28 m$ respectively, find the volume of air inside the godown. Also find the cost of roofing at the rate of $₹ 500 per square metre$ .

Important Questions on Mensuration

Learn and Prepare for any exam you want !

A godown is formed of a cuboid of dimensions 63 m×28 m×5 m covered by a half cylindrical roof. If the length and breadth of the cuboid are 63 m and 28 m respectively, find the volume of air inside the godown. Also find the cost of roofing at the rate of ₹500 per square metre.

Important Questions on Mensuration

Learn and Prepare for any exam you want !