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

Answers
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.

Answers
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.

Answers
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

Answers
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.

We hope the given RBSE Solutions for Class 8 Maths Chapter 15 Surface Area and Volume Additional Questions will help you. If you have any query regarding Rajasthan Board RBSE Class 8 Maths Chapter 15 Surface Area and Volume Additional Questions, drop a comment below and we will get back to you at the earliest.