Question

Ramesh has decided to build a swimming pool as shown in the figure on an empty plot 25 metres long and 15 metres wide. He is discussing with his son Mahesh about his plan to build the pool, put tiles on the bottom of the pool and other requirements of the pool. Can you help Mahesh to answer the following questions which his father has asked in the discussion?

(P.T.O)

Swimming Pool (cuboid)

(deep) 6 m

25 m

i. Find surface area of the pool?

a. 655 m?

b. 755 m?

15 m

c. 855 m2

d. 955 m2

ii. If Ramesh plans to cover the bottom and sides of the pool with square tiles having side 25cm, how many such tiles will be required?

a. 13,680

b. 14,680

c. 16,480

iii. If each tile costs 40 how much will be the total cost?

a. 5,42,700

b5,47,200

iv. What is volume of the pool?

a. 2050 m b. 2150 m

c6,42,700

c. 2250 m

d. 18,640

d6,47,200

d. 2350 m

v. A local digging company charges at the rate of 150 per cubic metre. How much Ramesh has to pay for digging the swimming pool?

a. 3,37,500 b. 3,47,500 c. 3,57,500 d. 3,67,500​

Answer 1

please send me the picture of the sum

Answer 2

i.) The surface area of the pool, $SA=855m^{2}$. (Option c)

ii.) The number of tiles required, $n=13,680$. (Option a)

iii.) Cost of tiles = ₹5,47,200. (Option b)

iv.) The volume of the pool, $V=2250m^{3}$. (Option c)

v.) Cost of digging the pool = ₹3,37,500. (Option a)

Given,

A cuboidal swimming pool with

Length, $l=25m$

Breadth, $b=15m$

Depth, $h=6m$

To find,

i.) The surface area of the pool.

ii.) Number square tiles with side, $s=25cm$ will be required.

iii.) Cost of total tiles used.

iv.) Volume of the pool.

v.) Price of digging the pool.

Solution,

i.)

We know that the lateral surface area of a cuboid is given by,

$LSA=2(l+b)h$

But since the pool is open from the top we will be requiring the surface area of four sides and the floor.

⇒$SA=2(l+b)h+lb$

So,

⇒$SA=2*6(25+15)+25*15$

⇒$SA=12(40)+375$

⇒$SA=480+375$

⇒$SA=855m^{2}$

Therefore, the surface area of the pool is $855m^{2}$. (Option c)

ii.)

Side of the square tile,

$s=25cm$

⇒$s=\frac{25}{100}m$

⇒$s=0.25m$

So, the surface area of the tile will be,

$A=s^{2}$

⇒$A=0.25^{2}$

⇒$A=0.0625m^{2}$

Hence, the number of tiles required to cover the bottom and sides of the pool will be,

The surface area of the pool is divided by the surface area of the tile.

⇒$n=\frac{SA}{A}$

⇒$n=\frac{855}{0.0625}$

⇒$n=13680 tiles$

Therefore, Ramesh requires 13,680 such tiles to cover the pool. (Option a)

iii.)

The total cost of the tiles will be,

Cost of one tile multiplied by the total number of tiles.
⇒$cost=13680*40$

⇒$cost=547200$

Therefore, 13,680 tiles would cost him ₹5,47,200. (Option b)

iv.)

We know that volume of cuboid is given by,

$V=l*b*h$

⇒$V=25*15*6$

⇒$V=2250m^{3}$

Therefore, the volume of the pool is $2250m^{3}$ . (Option c)

v.)

Since,

The rate of digging is 150 per cubic meter.

The total cost of digging the pool will be, the volume of the pool multiplied by the rate of digging.

⇒$C=2250*150$

⇒$C=337500$

Therefore, the cost of digging the pool would be ₹3,37,500. (Option a)