9th Maths

# Surface Area

## Exercise 13.1 Part 1

Question 1: A plastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is to be open at the top. Ignoring the thickness of the plastic sheet, determine:

- The area of the sheet required for making the box.
- The cost of sheet for it, if a sheet measuring 1m
^{2}costs Rs 20.

**Answer:** l = 1.5 m, b = 1.25 m, h = 0.65 m

Area of base `= lxxb = 1.5xx1.25 = 1.875 sq m`

Area of four walls `=2h(l + b)=2xx0.65(1.5 + 1.25)=1.3xx2.75 = 3.575 sq m`

Total area `= 1.875 + 3.575 = 5.45 sq m`

`Co\st\=Ra\te\xxAr\ea\= 20xx5.45 = Rs. 109`

Question 2: The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of Rs 7.50 per m^{2}

**Answer:** l = 5m , b = 4m, h = 3 m, rate = Rs. 7.50 per sq m

Area of roof `= lxxb = 5xx4 = 20 sq m`

Area of four walls `= 2h(l + b)= 2xx3(5 + 4)=6xx9 = 54 sq m`

Total area `= 20 + 54 = 74 sq m`

`Co\st = Ra\te\xx\Ar\ea\ = 7.50xx74 = Rs. 555`

Question 3: The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of Rs 10 per m^{2} is Rs 15000, find the height of the hall. [Hint : Area of the four walls = Lateral surface area.]

**Answer:** Perimeter = 250m, rate = Rs. 10 per sq m, cost = Rs. 15000, h = ?

`Ar\ea\ = (co\st)/(ra\te)= 1500/10 = 1500 sq m`

Area of four walls `= hxxperimeter`

Or, `1500 = hxx250`

Or, `h = 1500/250 = 6 m`

Question 4: The paint in a certain container is sufficient to paint an area equal to 9.375 m^{2}. How many bricks of dimensions 22.5 cm × 10 cm × 7.5 cm can be painted out of this container?

**Answer:** l = 22.5 cm, b = 10 cm, h = 7.5 cm, total area = 9.375 sq m = 93750 sq cm

Surface area of brick `=2(lb+bh+lh)``=2(22.5xx10+10xx7.5+22.5xx7.5)`

`= 2(225 + 75 + 168.75)`

`= 2xx468.75 = 937.50 sq cm`

Hence, number of bricks `= 93750/937.50 = 100`

Ex 13.1 Part 1

Ex 13.1 Part 2

Ex 13.2 Part 1

Ex 13.2 Part 2

Ex 13.3 Part 1

Ex 13.3 Part 2

Ex 13.4 Part 1

Ex 13.4 Part 2