## RS Aggarwal Class 9 Solutions Chapter 13 Volume and Surface Area Ex 13A

These Solutions are part of RS Aggarwal Solutions Class 9. Here we have given RS Aggarwal Class 9 Solutions Chapter 13 Volume and Surface Area Ex 13A.

**Other Exercises**

- RS Aggarwal Solutions Class 9 Chapter 13 Volume and Surface Area Ex 13A
- RS Aggarwal Solutions Class 9 Chapter 13 Volume and Surface Area Ex 13B
- RS Aggarwal Solutions Class 9 Chapter 13 Volume and Surface Area Ex 13C
- RS Aggarwal Solutions Class 9 Chapter 13 Volume and Surface Area Ex 13D

**Question 1.**

**Find the volume, the lateral surface area and the total surface area of the cuboid whose dimensions are :**

**(i) length = 12cm, breadth = 8cm and height = 4.5cm**

**(ii) length = 26 m, breadth = 14m and height = 6.5m**

**(iii) length = 15m, breadth = 6m and height = 5dm**

**(iv) length = 24m, breadth = 25cm and height = 6m**

**Solution:**

(i) Length of cuboid (l) = 12cm

Breadth (b) = 8cm

and height (h) = 4.5cm

**Question 2.**

**Find the capacity of a closed rectangular cistern whose length is 8m, breadth 6m and length 2.5m. Also find the area of the non sheet required to make the cistern.**

**Solution:**

Length of closed rectangular cistern (l) = 8m

breadth (b) = 6m

and depth (b) = 2.5m.

(i) .’. Volume of cistern = l.b.h.

= 8 x 6 x 2.5 m³ = 120m³

(ii) Total surface area = 2(lb + bh + hl)

= 2(8 x 6 + 6 x 2.5 + 2.5 x 8) cm²

= 2(48 + 15 + 20)

= 2 x 83 m²

= 166 m² Ans.

**Question 3.**

**The dimensions of a room are (9m + 8m x 6.5m). It has one door of dimensions (2m x 1.5m) and two windows each of dimensions (1.5 x 1m). Find the cost of whitewashing the walk at Rs. 6.40 per square metre.**

**Solution:**

Length of room (l) = 9m

Breadth (b) = 8m

and height (h) = 6.5m

**Question 4.**

**How many planks of dimensions (5m x 25cm x 10cm) can be stored in a pit which is 20m long, 6m wide and 80cm deep ?**

**Solution:**

Length of pit (l) = 20m

Breadth (b) = 6m

**Question 5.**

**How many bricks will be required to construct a wall 8m long, 6m high and 22.5 cm thick if each brick measures (25m x 11.25 cm x 6cm) ?**

**Solution:**

Length of wall (l) = 8m.

Width (b) = 22.5 cm =

and height (h) = 6m.

Volume of wall = l.b.h.

**Question 6.**

**A wall 15m long, 30 cm wide and 4m high is made of bricks, each measuring (22cm x 12.5cm x 7.5 cm). If of the total volume of the wall consists of mortar how many bricks are there in the wall ?**

**Solution:**

Length of wall (l) = 15m.

Width (b) = 30cm =

Height (h) = 4m

**Question 7.**

**An open rectangular cistern when measured from outside is 1.35 m long, 1.08 m broad and 90 cm deep. It is made up of iron, which is 2.5cm thick. Find the capacity of the cistern and the volume of the iron used.**

**Solution:**

Outer length of opened cistern = 1.35m = 135 cm

Breadth = 1.08 m = 108 cm

Depth = 90cm

Thickness of iron = 2.5cm.

**Question 8.**

**A river 2m deep and 45 m wide is flowing at the rate of 3 km per hour. Find the volume of water that runs into the sea per minute.**

**Solution:**

Depth of river = 2m

width = 45m.

Length of current in 60 minutes = 3km

**Question 9.**

**A box made of sheet metal costs Rs. 1620 at Rs. 30 per square metre. If the box is 5m long and 3m wide, find its height.**

**Solution:**

Total cost of box = Rs. 1620

Rate per sq. m = Rs. 30

**Question 10.**

**Find the length of the longest pole that can be put in a room of dimensions (10m x 10m x 5m).**

**Solution:**

Length of room (l) = 10m

Breadth (b) = 10m

Height (h) = 5m

**Question 11.**

**How many persons can be accommodated in a dining hall of dimensions (20m x 16m x 4.5m) assuming that each person requires 5 cubic metres of air ?**

**Solution:**

Length of hall (l) = 20m

Breadth (b) = 16m

and height (h) = 4.5m.

Volume of the air inside the hall

**Question 12.**

**A classroom is 10m long, 6.4 m wide and 5m high. If each student be given 1.6 m² of the floor area, how many students can be accommodated in the room ? How many cubic metres of air would each student get ?**

**Solution:**

Length of class room (l) = 10m

Width (b) = 6.4 m

Height (h) = 5m.

**Question 13.**

**The volume of a cuboid is 1536 m³ . Its length is 16m and its breadth and height are in the ratio 3 : 2. Find the breadth and height of the cuboid.**

**Solution:**

Volume of cuboid = 1536 m³

Length (l) = 16m

Ratio in breadth and height = 3:2

Let breadth (b) = 3x

their height (h) = 2x

**Question 14.**

**The surface area of a cuboid is 758 cm² . Its length and breadth are 14 cm and 11 cm respectively. Find its height.**

**Solution:**

Length of cuboid (l) = 14 cm

Breadth (b) = 11 cm .

Let height (h) =x cm

Surface area = 2(lb + bh + hl)

**Question 15.**

**Find die volume, the lateral surface area, the total surface area and the diagonal of a cube, each of**

**whose edges measures :**

**(a) 9m, (b) 6.5 cm. (Take √3 = 1.73)**

**Solution:**

(a) Edge of cube (a) = 9m .

(i) volume = a³ = (9)³ m³ = 729 m³

(ii) Lateral surface area = 4a²

**Question 16.**

**The total surface area of a cube is 1176 cm² . Find its volume.**

**Solution:**

Total surface area of a cube = 1176 cm²

Let each edge he ‘a’

then 6a² =1176

**Question 17.**

**The lateral surface area of a cube is 900 cm². Find its volume.**

**Solution:**

Lateral surface area of a cube = 900 cm²

Let ‘a’ be the edge of the cube

**Question 18.**

**The volume of a cube is 512 cm³. Find its surface area.**

**Solution:**

Volume of a cube = 512 cm³

Let ‘a’ be its edge, then

**Question 19.**

**Three cubes of metal with edges 3cm, 4 cm and 5 cm respectively are melted to form a single cube. Find the lateral surface area of the new cube formed.**

**Solution:**

Edge of first-cube = 3 cm.

Volume = (3)³ = 27 cm³

**Question 20.**

**In a shower, 5cm of rain falls. Find the volume of water that falls on 2 hectares of ground.**

**Solution:**

Area of ground = 2 hectares

= 2 x 10000 = 20000 m²

Height of rain falls 5cm = m

∴ Volume of rain water = 20000 x m³

= 1000 m³ Ans.

Hope given RS Aggarwal Class 9 Solutions Chapter 13 Volume and Surface Area Ex 13A are helpful to complete your math homework.

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