Page 280 - ICSE Math 8

Self-Testing Exercise 5

MENSURATION

1. The diagonal of a square is 14 cm long. Find the length of its side and area.

2. A garden consists of a rectangular flower bed surrounded by 3 m wide path. The length and the breadth
of the flower bed are 48 m and 40 m respectively. Find the length of the wire required to fence the
boundary of the garden.

3. Find the area of the following figures.

(a) D 28 m (b) 20 m
C
15 m 9 m 10 m
26 m 20 m
A B
40 m

4. Each side of a rhombus is 61 cm long and one of its diagonals is 120 cm. Find the length of the other
diagonal and the area of the rhombus.

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5. The area of a trapezium is 572 m and the distance between its two parallel sides is 11 m. If one of its
parallel sides is shorter than the other by 6 m, find the length of its parallel sides.

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6. The cost of fencing a rectangular park of length 72 m at the rate of ` 8 per m is ` 1,840. Find the width
of the park.
7. The sum of the areas of two small circles is equal to the area of a bigger circle of radius 13 cm.
If the diameter of one of the small circles is 24 cm, find the radius and area of the second circle.
(Use π = 3.14)

8. A path of uniform width 2.5 m surrounds a rectangular park with dimensions 20 m × 16 m. Find the
area of the path.
2
2
9. The areas of two concentric circles are 186 cm and 172 cm . Find the difference between the radii of
the two circles.
10. The length, breadth and height of a cuboid are in the ratio 5 : 4 : 3. If the volume of the cuboid is
3
7,500 cm , find its surface area and the length of the diagonal.

11. A metallic cuboid with dimensions 48 cm × 44 cm × 52 cm is melted and recasted into identical cuboids
with dimensions 12 cm × 11 cm × 13 cm. Find the number of cuboids formed.

12. The external dimensions of a closed metallic box are 35 cm, 28 cm and 25 cm. If the walls of the box
are 2 cm thick, find:
(a) the capacity of the box (b) the volume of the metal used
3
(c) the weight of the box, if 1 cm of the metal weighs 0.25 g

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