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Practice each question, then open the answer or worked solution.
The volume of a cube is 64 cm3. Its surface area is
(a) 16 cm2 (b) 64 cm2 (c) 96 cm2 (d) 128 cm2
Solution: The correct answer is option (c) 96 cm2
Explanation:
Let “a” be the side of the cube
Given that, the volume of a cube is 64 cm3
It means that a3 = 64 cm3
Hence, a = 4 cm
Therefore, the surface area of a cube = 6 x 42 = 6 x 16 = 96
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
Solution: The correct answer is option (d) one third
Explanation:
We know that the curved surface area of a cylinder is 2πrh, when the radius is “r”, and the height is “h”.
Let “H” be the new height.
When the radius of a cylinder is tripled, then the CSA of a cylinder becomes,
CSA = 2π (3r) H
CSA = 6πr. H
Now, compare the CSA of the cylinder to find the height
6πrH = 2πrh
H = 2πrh / 6πr
H = (1/3)h
Hence, the new height of the cylinder is one-third of the original height.
How many small cubes with edges of 20 cm each can be just accommodated in a cubical box of 2 m edge?
(a) 10 (b) 100 (c) 1000 (d) 10000
Solution: The correct answer is option (c) 1000
Explanation:
We know that the volume of a cube is (side)3
Therefore, the volume of each small cube is (20)3
= 8000 cm3
When it is converted into m3, we get
V = 0.008 m3
It is given that the volume of the cuboidal box is 23 = 8 m3
Now, the number of small cubes that can be accommodated in the cuboidal box is
= 8/ 0.008 = 1000
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
Solution: The correct answer is option (c) πr3
Explanation:
The volume of the cylinder = πr2 h
Given that r = h
Then, the volume of cylinder = πr2 (r)
V = πr3
The volume of a cube whose edge is 3x is
(a) 27x3 (b) 9x3 (c) 6x3 (d) 3x3
Solution: The correct answer is option (a) 27x3
Explanation:
The volume of a cube is (side)3
V = (3x)3
V = 27x3
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
Solution: The correct answer is option (B) 36 cm2
Explanation:
From the given figure, it is clear that a quadrilateral ABCD is a parallelogram. Here, the diagonal AC divides the parallelogram into two equal triangles.
Hence, the area of a triangle ABC = (1/2) bh
Here, b = 12 and h = 3
= (1/2) (12)(3)
= 18
Therefore, the area of a parallelogram ABCD = 2 (18) = 36 cm2
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
Solution: The correct answer is option (c) 24 cm2
Explanation:
From the given figure, the diagonal AC divides the rhombus into two triangles of equal area.
Therefore, the area of a triangle ABC = (1/2) bh
= (1/2) (4) (6)
=12 cm2
Therefore, the area of a rhombus ABCD = 2(12) = 24
The area of a parallelogram is 60 cm2, and one of its altitudes is 5 cm. The length of its corresponding side is
(a) 12 cm (b) 6 cm (c) 4 cm (d) 2 cm
Solution: 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
The perimeter of a trapezium is 52 cm, and its each non-parallel side is equal to 10 cm with a height 8 cm. Its area is
(a) 124 cm2 (b) 118 cm2 (c) 128 cm2 (d) 112 cm2
Solution: 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
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
Solution: 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