#### Class Nine Maths Chapter 13 NCERT Solutions Areas

## Chapter 13: Surface Areas and Volumes

**TEXTBOOK’S
EXERCISE – 13.5 **

**1. A matchbox measures 4 cm × 2.5 cm × 1.5 cm. What will be the volume of a packet containing 12 such boxes? **

**Sol.
**Here, l = 4 cm, b = 2.5 cm, h = 1.5 cm

Volume of 1 matchbox

= *lbh *= 4 × 2.5 × 1.5 cm3 = 15 cm3

Volume of 12 matchboxes

= 15 × 12 cm3 = 180 cm3

**2. A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many litres of water can it hold? (1 m3 = 1000 l) **

**Sol.
**Here, l = 6 m, b = 5 m, h = 4.5 m

Volume of the tank = lbh

= 6 × 5 × 4.5 m^{3}
= 135 m^{3}

= 135 × 1000 litres
= 1,35,000 litres. (Since 1 m^{3} = 1000 litres)

Hence, the tank can hold 1,35,000 litres of water.

**3. A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid? **

**Sol.
**Here, l = 10 m, b = 8 m, h = ?

The volume of the vessel = lbh

⇒ 380 = 10 × 8 × h

Hence, the tank must be made 4.75 m high

**TEXTBOOK’S EXERCISE – 13.5 **

**4. Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of Rs 30 per m**^{3}**.**

**Sol.
**l = 8 m, b = 6 m, h = 3 m

The volume of the pit

= lbh = 8 × 6 × 3 m^{3} = 144
m3

Cost of digging 1m^{3}
= Rs 30

∴ Cost of digging 144 m^{3} = Rs 30
× 144

= Rs 4320

**5. The capacity of a cuboidal tank is 50000 litres of water. Find the breadth of the tank, if its length and depth are respectively 2.5 m and 10 m. **

**Sol.
**Here, l = 2.5 m, h = 10 m, b = ?

The capacity of the tank

Also, the capacity of the tank = lbh

⇒ 50 = 2.5 × b × 10 ⇒ b = 50 25 = 2

Hence, the breadth of the tank = 2 m