RBSE Class 8 Maths Important Questions Chapter 11 Mensuration

Rajasthan Board RBSE Class 8 Maths Important Questions Chapter 11 Mensuration Important Questions and Answers.

RBSE Class 8 Maths Chapter 11 Important Questions Mensuration

Multiple Choice Questions:

Question 1.
The length of the diagonals of a rhombus are 10 m and 12 m. The area of the given parallelogram is:
(a) \(\frac{10+12}{2}\)
(b) 10 × 12
(c) \(\frac{1}{2}\) × (12 + 10)
(d) \(\frac{1}{2}\) × 10 × 12
Answer:
(d) \(\frac{1}{2}\) × 10 × 12

Question 2.
The length, breadth and height of a box are 20 cm, 10 cm and 5 cm respectvely. The 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)
Answer:
(b) 2(20 × 10 + 10 × 5 + 5 × 20)

Question 3.
Each edge of a given cube is of length 10 m. The surface area of the given cube will be:
(a) 600 m²
(b) 100 m²
(c) 500 m²
(d) 400 m²
Answer:
(a) 600 m²

Question 4.
The surface area of a cube is 36 cm2. The edge of the given cube will be:
(a) √9 cm
(b) √8 cm
(c) √6 cm
(d) √10 cm
Answer:
(c) √6 cm

Question 5.
The base area of a cuboid is 140 m² and height is 3 m. Volume of the given cuboid is:
(a) 140 × 3 m³
(b) \(\frac{140}{3}\) m³
(c) (140 + 3) m³
(d) [(140)² - (3)²] m³
Answer:
(a) 140 × 3 m³

Question 6.
Each edge of a given cube is of length 4 cm. The volume of the given cube will be:
(a) (4)²
(b) (4)³
(c) (4)⁴
(d) (4)⁵
Answer:
(b) (4)³

Question 7.
The curved surface area of a cylinder is:
(a) πr²h
(b) 2πr(h + r)
(c) 2πrh
(d) 2πr
Answer:
(c) 2πrh

Question 8.
The radius and height of a cylinder are 3 cm and 10 cm respectively. The volume of the given cylinder is _________
(a) π(3)² × (10) cm³
(b) 2πr(3) (10) cm²
(c) 2π(3)² (10) cm³
(d) π(3)2 cm²
Answer:
(a) π(3)² × (10) cm³

Fill in the blanks:

Question 1.
_______ of a solid is the sum of the area of its faces.
Answer:
Surface area

Question 2.
Surface area of four walls of the room = 2 × _______ (b + l)
Answer:
h

Question 3.
The amount of region occupied by a solid is called its _______
Answer:
volume

Question 4.
1 m3 = _______ L
Answer:
1000

Question 5.
_______ = 1 mL
Answer:
1 cm3

Question 6.
1 L = _______ cm³
Answer:
1000.

Very Short Answer Type Questions:

Question 1.
Find the area of a rhombus whose diagonals are 10 cm and 8.2 cm.
Answer:
Area of rhombus = \(\frac{1}{2}\) × (Product of the diagonals)
= \(\frac{1}{2}\) × 10 × 8.2
= 41 cm²

Question 2.
Find the surface area of a brick measuring 25 cm × 12 cm × 10 cm.
Answer:
Surface area of brick
= 2(25 × 12 + 12 × 10 + 10 × 25)
= 2(300 + 120 + 250)
= 2 × 670
= 1340 cm²

Question 3.
The side of a cube measures 1 cm. Two such cubes are glued together. Find the total surface area of the solid shape so formed.
Answer:
2(2 +1 + 2) cm2 = 2 × 5 = 10 cm²

Question 4.
Find the volume of a cuboid whose length, breadth and height are 15 cm, 10 cm and 8 cm respectively.
Answer:
Volume of cuboid = l × b × h = 15 × 10 × 8 = 1200 cm³

Question 5.
A rooms internal measurements are 12 m x 8 m x 4 m. Find die area of its four walls.
Answer:
l =12m, b = 8m, h = 4m
Area of four walls of room = 2(l + b) × h
= 2(12 + 8) × 4 = 40 × 4 = 160 m²

Question 6.
Find the height of a cylinder whose radius is 7 cm and total surface area is 968 cm².
Answer:
Height of cylinder = h, radius (r) = 7 cm
Surface area = 2πr (h + r)
⇒ 968 = 2 × \(\frac{22}{7}\) × 7(h + r)
⇒ h + 7 = \(\frac{968}{44}\)
⇒ h= 22 - 7
⇒ h = 15 cm

Essay Type Questions:

Question 1.
The floor of a building consists of 3000 tiles which are shombus shaped and each of its diagonals are 45 cm and 30 cm in length. Find the total cost of polishing the floor, If the cost per m2 is Rs. 5.
Answer:
Area of the floor = 3000 × Area of one tile
= 3000 × \(\frac{1}{2}\) × 45 × 30 cm²
= 1500 × 45 × 30 cm²
= \(\frac{1500 \times 45 \times 30}{100 \times 100}\) m²
= 202.5 m²

Cost of polishing the floor @ 5 per m²
= Rs. (5 × 202.5)
= Rs. 1012.50

Question 2.
In a building there are 20 cylindrical pillars. The radius of each pillar is 14 cm and height in 4 m. Find the total cost of painiting the curved surface area of all pillars at the rate of Rs. 10 per m².
Answer:
Radius of cylindrical pillar,
r- 14 cm. = 0.14 m
height, h = 4 m

Curved surface area of a cylinder = 2πrh
Curved surface area of a pillar
k =2 × \(\frac{22}{7}\) × 0.14 × 4
= 3.52 m²

Curved surface area of 20 such pillar
= 3.52 × 20 = 70.4 m²

Cost of painting an area of 1 m² = Rs 10
Therefore, cost of painting 70.4 m²
= 70.4 × 10 = Rs. 704

Question 3.
The length, breadth and height of a Cuboidal room are 12 m, 8 m and 4 m respectively. Find the cost of whitewash on four walls and ceiling if the cost of whitewash per square metre in Rs. 5.
Answer:
Length of room = 12 m Breadth = 8 m and Height = 4 m ,
Area of four walls = 2 × H (L + B)
= 2 × 4 (12 + 8)
= 8 × 20 = 160 m²

Area of roof = L × B
= 12 × 8 = 96 m²
∴ Area for whitewash = 160 + 96 = 256 m²
It is given that the cost of whitewash per square metre = Rs. 5
∴ The cost of whitewash = 256 × 5 = Rs. 1280