# RBSE Solutions for Class 8 Maths Chapter 15 Surface Area and Volume Additional Questions

RBSE Solutions for Class 8 Maths Chapter 15 Surface Area and Volume Additional Questions is part of RBSE Solutions for Class 8 Maths. Here we have given Rajasthan Board RBSE Class 8 Maths Chapter 15 Surface Area and Volume Additional Questions.

 Board RBSE Textbook SIERT, Rajasthan Class Class 8 Subject Maths Chapter Chapter 15 Chapter Name Surface Area and Volume Exercise Additional Questions Number of Questions 33 Category RBSE Solutions

## Rajasthan Board RBSE Class 8 Maths Chapter 15 Surface Area and Volume Additional Questions

I. Objective Type Questions

Question 1.
The dimensions of a box are 20 cm. × 10 cm. × 5 cm. The total surface area of box is
(a) 20 × 10 × 5
(b) 2(20 × 10 + 10 × 5 + 5 × 20)
(c) 2(20 +10 + 5)
(d) 2(20 × 10 × 5)

Question 2.
Side of a cube is 10 m. Total surface area of cube is
(a) 600 m²
(b) 100 m²
(c) 500 m²
(d) 400 m²

Question 3.
Total surface (RBSESolutions.com)area of a cube is 36 cm.². Side of a cube is
(a) √9 cm.
(b) √8 cm.
(c) √6 cm.
(d) √10 cm.

Question 4.
The area of base of a cuboid is 140 m² and height is 3 m. Then volume of cuboid is
(a) 140 x 3 m3
(b) $$\frac { 140 }{ 3 }$$ m3
(c) (140 + 3) m3
(d) [(140)² – (3)²] m3

Question 5.
The side of a cube is 4 cm. and volume of cube (in cm.3) is
(a) (4)2
(b) (4)3
(c) (4)4
(d) (4)5

Question 6.
Curved surface area of a cylinder is
(a) πr²h
(b) 2πr(h + r)
(c) 2πrh
(d) 2πr

Question 7.
If the radius of a cylinder is 3 cm. and height is 10 cm., then volume is
(a) π(3)2 x (10) cm.3
(b) 2π(3) (10) cm.2
(c) 2π(3)2 (10) cm.3
(d) π(3)2 cm 2

Question 8.
Side of a cube is 1 cm. If we join 2 cubes of side 1 cm., then the(RBSESolutions.com)total surface area is
(a) 6 cm.²
(b) 10 cm.²
(c) 12 cm.²
(d) 20 cm.²

1. (b)
2. (a)
3. (c)
4. (a)
5. (b)
6. (c)
7. (a)
8. (b)

II. Fill in the blanks

Question 1.
Space occupied by any solid is called its___

Question 2.
The quantity of liquid in a three dimensional pot is called___

Question 3.
Area of four(RBSESolutions.com)walls of a room = 2 x (l + b) x ___

Question 4.
Surface area of a solid is equal to___of all areas of its faces.

Question 5.
1 m3 =___litre.

1. Volume
2. Capacity
3. h
4. Sum
5. 1000

III. True/False Type Questions

Question 1.
1 cm3 = 1 mL

Question 2.
1 L = 1000 cm3

Question 3.
The $$\frac { 2 }{ 3 }$$ part of volume of a tank of dimension 6m x 5m x 4m is 80 m3.

Question 4.
The volume of a cylindrical poll, whose height is 7 m and diameter is 12 cm, is π (6)² x 7 cm3.

1. True
2. True
3. True
4. False.

IV. Matching Type Questions

 Part 1 Part 2 1. Number of vertices of a cube (a) 6 m 2. Number of edges of a cube (b) 2 3. Number of edges of cylinder (c) 12 4. Side of a cube of volume 216 m³ (d) 8

1. ↔ (d)
2. ↔ (c)
3. ↔ (b)
4. ↔ (a)

V. Very Short Answer Type Questions

Question 1.
Why is it wrong to say that given shape is a cylinder?
Solution
A cylinder has two edges and(RBSESolutions.com)congruent circles. Here circles are not congruent. Therefore this figure is not a cylinder.

Question 2.
The ratio of two cylindrical poles is 3 : 2 and ratio of their height is 2 : 3. Find the ratio of curved surface area of poles.
Solution

= $$\frac { 1 }{ 1 }$$
= 1 : 1

Question 3.
The area of three adjacent faces of a cuboid are p, q and r. The volume of cuboid is V. Prove that V² = pqr
Solution
Let l, b and h be the(RBSESolutions.com)dimensions of cuboid respectively. Then,
p = lb
q = bh
r = hl
∴ pqr = (lb) (bh) (hl)
= l²b²h²
= (lbh)²
= V²
⇒V² = pqr

VI. Short Answer Type Questions

Question 1.
If V is the volume of a cuboid of dimensions a, b and c and surface(RBSESolutions.com)area is S, then prove that
$$\frac { 1 }{ V } =\frac { 2 }{ S } \left( \frac { 1 }{ a } +\frac { 1 }{ b } +\frac { 1 }{ c } \right)$$
Solution

Question 2.
The population of a village is 2000. Every citizen needs 150 litre water per day. The dimensions of water tank is 20 m x 15 m x 6 m in village. For how many days this(RBSESolutions.com)tank is sufficient for village?
Solution
Volume of tank = 20 x 15 x 6 m3
= 1800 m3 ;
= 1800 x 1000 litre
Water requirement of village per day = 150 x 2000
= 3,00,000 litre
∴ Required number of days

Question 3.
How many bricks are required to make a wall of dimensions 12 m. length x 6 decimeter breadth x 4.5 m height. The dimension of one brick is 18 cm x 12 cm x 10 cm(RBSESolutions.com)and $$\frac { 1 }{ 10 }$$ Volume is covered by cement?
Solution—Volume of one brick
= 18 x 12 x 10
= 2160 cm.3
Volume of wall = 12 x 0.6 x 4.5
= 32.4 m3
| 6 decimeter = $$\frac { 6 }{ 10 }$$ meter = 0.6 meter
∴Volume covered by cement
= $$\frac { 1 }{ 10 }$$ x 32.4 = 3.24 m3
∴Volume of bricks
= 32.4 – 3.24
= 29.16 m3
= 29.16 x 1000000 cm.3
∴Number of bricks

= 13500

Question 4.
A closed iron tank of dimensions 12 m length, 9 m breadth and 4 m depth is to be made. The iron sheet is used whose cost is Rs 50 per meter and it is 2 m wide.
Solution
Surface area of tank
= 2 (12 x 9 + 9 x 4 + 4 x 12)
= 2 (108 + 36 + 48)
= 2 (192)
= 384 m²
Width of iron sheet = 2 meter
Length of iron sheet = $$\frac { 384 }{ 2 }$$
= 192 meter
Cost of iron sheet = 192 x 50
= Rs 9600

Question 5.
A cylinder, whose height is 3 m, is open(RBSESolutions.com)from top. The circumference of its base is 22 m. Find its total surface area.
Solution
Let the radius of base be r m. Then,
2πr = 22
⇒ 2 x $$\frac { 22 }{ 7 }$$ x r = 22
$$r=\frac { 7 }{ 2 }$$
h = 3 m
Total Surface Area
= 2 πrh + πr2
= $$2.\frac { 22 }{ 7 } .\frac { 7 }{ 2 } .3+\frac { 22 }{ 7 } .\frac { 7 }{ 2 } .\frac { 7 }{ 2 }$$
= 66 + 38.5
= 104.5 m²

Question 6.
A cylindrical pipe, which is open from both sides, is made of iron sheet of thickness 2 cm. If external diameter is 16 cm and height is 100 cm, then find the total iron used in making the pipe?
Solution
External diameter = 16 cm.
External(RBSESolutions.com)radius (R) = $$\frac { 16 }{ 2 }$$ cm.
= 8 cm.
Thickness of sheet = 2 cm.
∴ Inner radius (r) = 8 – 2 = 6 cm.
Height (h) = 100 cm.
∴ Used iron
= External Volume – Internal Volume
= πR²h – πr2h
= π (R² – r²) h
= $$\frac { 22 }{ 7 }$$ {(8)² – (6)²} 100
= $$\frac { 22 }{ 7 }$$ x 28 x 100
= 8800 cm.3

Question 7.
Find the length of longest rod, which can be put in a room of dimensions 12 m x 9 m x 8 m.
Solution
For room
l = 12 m
b = 9 m
h = 8 m
∴ Length of longest rod = Length of diagonal

Question 8.
The curved surface area of a cylindrical tank is 440 m². Its height is 4 m. Find volume of the tank.
Solution
Height of cylinder (h) = 4 m.
Curved surface area of cylinder = 440 m²
To find = Volume of cylinder
∵ Curved(RBSESolutions.com)Surface Area of cylinder = 440 m²
⇒ 2πrh = 440

= 3850 m²

Question 9.
The radius of a cylinder is 7 cm. and its height is 10 cm. Find the curved surface area and volume of the cylinder, (use π = $$\frac { 22 }{ 7 }$$)
Solution
Radius of cylinder (r) = 7 cm.
Height (h) = 10 cm.
Curved(RBSESolutions.com)Surface Area of cylinder = 2πrh

Question 10.
Curved surface area of a cylinder is 880 m², whose height is 10 m. Find volume of cylinder. (use π = $$\frac { 22 }{ 7 }$$)
Solution
The curved(RBSESolutions.com)surface area of cylinder = 880 sq. m
and height (h) = 10 meter
Hence 2πrh = 880 m

Question 11.
Determine side of a cube whose total surface area is 1014 cm². Find its volume also.
Solution
Let the side of cube be a cm.
Then the total surface area of cube
= 6a² .sq. m
According to question
6a² = 1014
a2 = $$\frac { 1014 }{ 6 }$$ = 169
a = √169 = 13 cm
Hence the side of cube = 13 cm
Volume(RBSESolutions.com)of cube = (side)3
Hence 13 x 13 x 13 = 2197 cm3

Question 12.
Radius and total surface area of a cylinder are 7 cm and 968 cm2 respectively. Find its height.(use π = $$\frac { 22 }{ 7 }$$)
Solution
Given,
Radius of cylinder (r) = 7 cm
Total Surface Area = 968 sq. cm.
Height (h) = ?
Total(RBSESolutions.com)surface area of cylinder = 2πr(h + r)
By putting values
968 = 2 x $$\frac { 22 }{ 7 }$$ 7(h + 7)
968 = 44(h + 7)
$$\frac { 968 }{ 44 }$$ = h + 7
22 = h + 7
h = 22 – 7
h = 15 cm.
∴ Height of cylinder = 15 cm.

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