#### Class nine NCERT Sol Maths Surface Areas Volumes

## Chapter 13: Surface Areas and Volumes

**TEXTBOOK’S
EXERCISE – 13.6 **

**1. The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. How many litres of water can it hold? (1000 cm3 = 1l) **

**Sol.
**Here, h = 25 cm, 2πr = 132 cm.

2πr = 132 ⇒ 2 × 22/7 × r = 132

= 21 cm

Volume of the cylinder = πr^{2}h

= 22/7 × 21 × 21 × 25 cm^{3} = 34650 cm^{3}

= 34.65 litres

**2. The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm3 of wood has a mass of 0.6 g. **

**Sol. **Here, inner radius (r) = 24/2 cm
= 12 cm

Outer radius (R) = 28/2 cm = 14 cm, h = 35 cm

Volume of the wood used in the pipe

= π(R^{2}
– r^{2}) h

= 22/7 [(14)^{2}
– (12)^{2}] × 35 cm^{3}

= 22/7 ×
26 × 2 × 35 cm^{3} = 5720 cm^{3}

Mass of 1 cm^{3}
of wood = 0.6 g

∴ Mass of 5720 cm3 of wood

= 0.6 × 5720 g = 3432 g

= 3.432 kg.

**3. A soft drink is available in two packs — (i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and (ii) a plastic cylinder with circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much? **

**Sol.
For tin can with rectangular base **

l = 5 cm, b = 4 cm, h = 15 cm

Volume of the tin can

= lbh = 5 × 4 × 15 cm^{3} = 300
cm^{3 }

**For
plastic cylinder with circular base **

r = 7/2 cm = 3.5 cm, h = 10 cm

Volume of the plastic
cylinder = πr^{2}h

= 22/7 ×
3.5 × 3.5 × 10 cm^{3} = 385 cm^{3}

Difference in the
capacities of the two containers = (385 – 300) cm^{3} = 85 cm^{3}

Hence, the plastic cylinder with circular base has greater capacity by 85 cm^{3}.