Check here the Latest detailed Answers and Solutions as per the latest guidelines of Exercise 13.6 - Chapter 13 Surface Areas & Volumes class 9 ncert solutions Maths - [2024-2025]

Exercise 13.6 - Chapter 13 Surface Areas & Volumes class 9 ncert solutions Maths - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Question 1:

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

Answer:

Let the radius of the cylindrical vessel be r.

Height (h) of vessel = 25 cm

Circumference of vessel = 132 cm

2πr = 132 cm

Volume of cylindrical vessel = πr²h

= 34650 cm³

= 34.65 litres

Therefore, such vessel can hold 34.65 litres of water.

Question 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.

Answer:

Inner radius (r₁) of cylindrical pipe =

Outer radius (r₂) of cylindrical pipe =

Height (h) of pipe = Length of pipe = 35 cm

Volume of pipe =

Mass of 1 cm³ wood = 0.6 g

Mass of 5720 cm³ wood = (5720 × 0.6) g

= 3432 g

= 3.432 kg

Question 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?

Answer:

The tin can will be cuboidal in shape while the plastic cylinder will be cylindrical in shape.

Length (l) of tin can = 5 cm

Breadth (b) of tin can = 4 cm

Height (h) of tin can = 15 cm

Capacity of tin can = l × b × h

= (5 × 4 × 15) cm³

= 300 cm³

Radius (r) of circular end of plastic cylinder =

Height (H) of plastic cylinder = 10 cm

Capacity of plastic cylinder = πr²H

Therefore, plastic cylinder has the greater capacity.

Difference in capacity = (385 − 300) cm³= 85 cm³

Question 4:

If the lateral surface of a cylinder is 94.2 cm² and its height is 5 cm, then find (i) radius of its base (ii) its volume. [Use π = 3.14]

Answer:

(i) Height (h) of cylinder = 5 cm

Let radius of cylinder be r.

CSA of cylinder = 94.2 cm²

2πrh = 94.2 cm²

(2 × 3.14 × r × 5) cm = 94.2 cm²

r = 3 cm

(ii) Volume of cylinder = πr²h

= (3.14 × (3)² × 5) cm³

= 141.3 cm³

Question 5:

It costs Rs 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of Rs 20 per m², find

(i) Inner curved surface area of the vessel

(ii) Radius of the base

(iii) Capacity of the vessel

Answer:

(i) Rs 20 is the cost of painting 1 m² area.

Rs 2200 is the cost of painting =

= 110 m² area

Therefore, the inner surface area of the vessel is 110 m².

(ii) Let the radius of the base of the vessel be r.

Height (h) of vessel = 10 m

Surface area = 2πrh = 110 m²

(iii) Volume of vessel = πr²h

= 96.25 m³

Therefore, the capacity of the vessel is 96.25 m³ or 96250 litres.

Question 6:

The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?

Answer:

Let the radius of the circular end be r.

Height (h) of cylindrical vessel = 1 m

Volume of cylindrical vessel = 15.4 litres = 0.0154 m³

⇒ r = 0.07 m

Therefore, 0.4708 m² of the metal sheet would be required to make the cylindrical vessel.

Question 7:

A lead pencil consists of a cylinder of wood with solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.

Answer:

Radius (r₁) of pencil == 0.35 cm

Radius (r₂) of graphite = = 0.05 cm

Height (h) of pencil = 14 cm

Volume of wood in pencil =

Question 8:

A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients?