A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The side of the cube is
(a) 6 cm (b) 8 cm (c) 12 cm (d) 24 cm
The correct answer is option (a) 6 cm
Explanation:
Given that, the metal sheet dimension is 27 cm long, 8 cm broad and 1 cm thick.
Thus, the volume of the sheet = (27)(8)(1) = 216 cm3
It is given that, the metal sheet is melted to make a cube
Let the edge be “a”
Hence, a3 = 216 cm3
a = 6 cm
Area of a quadrilateral ABCD is 20 cm2 and perpendiculars on BD from opposite vertices are 1 cm and 1.5 cm. The length of BD is
(a) 4 cm (b) 15 cm (c) 16 cm (d) 18 cm
The correct answer is option (c) 16 cm
Explanation:
Given that, the area of a quadrilateral = 20 cm2
We know that, the area of a quadrilateral = (1/2) (diagonal) (sum of the altitudes)
20 = (1/2) (1+1.5) BD
20 = (1/2) (2.5) BD
20×2 = 2.5 BD
40 = 2.5 BD
BD = 16 cm
The perimeter of a trapezium is 52 cm and its each non-parallel side is equal to 10 cm with its height 8 cm. Its area is
(a) 124 cm2 (b) 118 cm2 (c) 128 cm2 (d) 112 cm2
The correct answer is option (c) 128 cm2
Explanation:
Given:
The perimeter of a trapezium = 52 cm
The sum of its parallel sides = 52 – (10+10) = 32 cm
We know that, the area of a trapezium = (1/2) (a+b) h
A = (1/2) (32) (8)
A = 128 cm2
The area of a parallelogram is 60 cm2 and one of its altitude is 5 cm. The length of its corresponding side is
(a) 12 cm (b) 6 cm (c) 4 cm (d) 2 cm
The correct answer is option (a) 12 cm
Explanation:
The area of a parallelogram = base x altitude
b. h = A
b (5) = 60
b = 60/5
b = 12cm
What is the area of the rhombus ABCD below if AC = 6 cm, and BE = 4cm?
(a) 36 cm2 (b) 16 cm2 (c) 24 cm2 (d) 13 cm2
The figure ABCD is a quadrilateral in which AB = CD and BC = AD. Its area is
(a) 72 cm2 (b) 36 cm2 (c) 24 cm2 (d) 18 cm2
The volume of a cube whose edge is 3x is
(a) 27x3 (b) 9x3 (c) 6x3 (d) 3x3
The correct answer is option (a) 27x3
Explanation:
The volume of a cube is (side)3
V = (3x)3
V = 27x3
The volume of a cylinder whose radius r is equal to its height is
(a) 1/4 πr3 (b) πr3/32 (c) πr3 (d) πr3/8
How many small cubes with edge of 20 cm each can be just accommodated in a cubical box of 2 m edge?
(a) 10 (b) 100 (c) 1000 (d) 10000
If the radius of a cylinder is tripled but its curved surface area is unchanged, then its height will be
(a) tripled (b) constant (c) one sixth (d) one third
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