Math Assignment  Class VIII Mensuration ch-14

Important extra questions on mensuration class VIII strictly according to the DAV board and CBSE Board, necessary for board examinations.

Question 1 

Find the length of the side of a rhombus whose diagonals are of lengths 12 cm and 16 cm.

Ans. Side of rhombus = 10 cm.

Question 2

The diameter of the roller is 5m and its length is 2.8m. It takes 8 complete revolutions to level the floor of a room. Find the area of the floor of the room.

Ans. 352 m²

Question 3 

The lengths of adjacent sides of a rectangle are in the ratio 3:4. If the length of its diagonal is 10 cm, find the length of sides of the rectangle.

Ans. 6 cm and 8 cm

Question 4

The length of a pair of adjacent sides of a rectangle are in the ratio 4 : 3. If its diagonal is of length 50 cm, find the lengths of the sides of the rectangle and hence find the perimeter of the rectangle.

Ans. Sides are 40 cm and 30 cm, Perimeter = 140 cm.

Question 5

The length, breadth and height of a solid cuboid are in the ratio 5 : 4 : 2. Its total surface area is 1216 cm². Find

(i) The dimension of the cuboid.

(ii) Volume of cuboid.

Ans. Dimensions are 20 cm, 16 cm, 8 cm, Volume = 2560 cm³.

Question 6

The volume of a metallic cylindrical pipe is 748 cm². Its length is 14 cm and its external radius is 9 cm. Find its thichness of the metal used.

Ans. Inner radius = 8 cm and Thicknes = 9cm - 8cm = 1 cm

Question 7

A cylinder of curved surface area 1152 m² is formed from a rectangular metallic sheet. Find the dimensions of the rectangular sheet if its length is double of its breadth.
Ans. Dimensions of rectangle are 24 m and 48 m
Solution Hint

ATQ

CSA of Cylinder = Area of rectangle = 1152m² 
2h ✕ h = 1152 m²  ⇒ h = 24m

2h = 2 ✕ 24 = 48m

Dimensions of rectangle are 24 m and 48 m

Question 8

Find the length of the side of a rhombus whose diagonals are of lengths 12 cm and 16 cm.

Ans. Side of rhombus = 10 cm.

Question 9

The thickness of a hollow metallic cylinder is 2 cm. It is 42 cm long and its inner radius is 10 cm. Find the volume of metal required to make the cylinder, assuming it is open at both the ends.

Ans. 5808 m³

Question 10 

The length, breadth and height of a room are 4.5 m, 3m and 350 cm respectively. Find the expenditure of plastering the walls and the ceiling of the room at the rate of 8 per square metre.

Ans. 66 m²

Question 11 

The ratio of the radius and height of a solid cylinder is 2 : 3. If its volume is 12936 cm³, find the total surface area of the cylinder.

Ans. 3080 cm²

Solution Hint

Let radius(r) = 2x, let Height (h) = 3x

Volume = 12936 cm³,

⇒ πr² h=12936

⇒ (22/7)✕2x✕2x✕3x = 12936

⇒ x³  = 343 

⇒ x = 7 cm

⇒ Radius = 2 ✕7 = 14 cm and Height = 3 ✕ 7 = 21 cm

Total Surface Area of Cylinder = 2πr(r + h)

                                                     = 3080 cm².

Question 12 

The cross-section of a canal of depth 9 m is in the form of a trapezium. If the width of the top of the canal is 4 m longer than its base and the area of cross-section is 72 m², then find the dimensions of top and bottom of the canal.

Ans.  Width of the top = 10 cm

Width of the base = 6 cm

Question 13 

The length of a cold storage is double its breadth. Its height is 3 metres and area of its four walls (including doors) is 108 m². Find its volume.

Ans. 216 m³.

Solution Hint

Let Breadth = x m,  Let Leangth = 2x m

Area of 4 walls = 108 m².

2(L + B) ✕ h = 108

⇒ x = 6

⇒ Breadth = 6 m and Leangth = 12 m

Volume of Cuboid = l ✕ b ✕ h

                             = 12 ✕ 6 ✕ 3 = 216 m³.

Question 14 

Sachin is painting 2 identical boxes. He paints the top and bottom of each box with red colour and the remaining four faces with blue colour. If the dimensions of each box is l x b x h, then find the total area of boxes painted in blue colour.

Ans. Area painted with red color = 4(l ✕ b) m².

         Area painted with blue color = 8(l + b) ✕ h m².

Question 15 

Ajay needs to cover 10 cylindrical shaped pen stands each of height h cm and radius r cm using a paper. How much paper is required for covering 10 pen stands ?

Ans. 10[2πrh + πr²].

Question 16 

It costs 2200 to paint the inner curved surface of cylindrical vessel 10 mn deep. If it is painted at the rate of R 20 per square metre then find

(1) The inner curved surface area of vessel

(2) Radius of base

(3) Capacity of vessel

Question 17 

A milk tank is in the form of a cylinder whose radius is 1.5 m and height is 7 m. Find the quantity of milk in litres that can be stored in the tank.

Question 18 

The perimeter of a trapezium is 52 cm and its two non parallel sides are of length 10 cm each. If the distance between two parallel sides is 8 cm, then, find the area of the trapezium.

Ans. 168 cm²

Question 19

The dimensions of a cuboid are in the ratio of 1 : 2 : 3 and its total surface area in 88 m². Find the dimensions.

Question 20

A company packages its milk powder in cylindrical containers whose base has a diameter of 16.8 cm and height 20.5 cm. Company places a label 1.5 cm from the top and the bottom around the curved surfaces of the container, as shown.

On the above information answer the following questions:

(i) Radius of the base of container is

(a) 8.4 cm         (b) 33.6 cm        (c) 16.8 cm            (d) 20.5 cm

(ii) Height of the label is

(a) 20.5 cm      (b) 19 cm           (c) 17.5 cm            (d) 23.5 cm

(iii) Area of the label is

(a) 1145.76 cm²                  (b) 924 cm²

(c) 1367.52 cm²                  (d) 1082.4 cm²

(iv) Volume of the container is:

(a) 4546.08 cm³               (b) 924 cm³

(c) 3880.8 cm³                (d) 541.2 cm³

(v) Total surface area of the container is

(a) 2πrh          (b) 2πr(r + h)        (c) 2πrh + πr²      (d)  πr² h

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