Cube and Cuboid
Question
Q1.
The length and breadth of an cuboid is increase in 5% and 4% , find the increase in % of the volume of cuboid.
(a) 9.4% (b) 9.2% (c) 6% (d) 8%
Solution.
(b) 9.2%
Solution
Q2.
Diagonal of cube √12 m. Find its lateral surface area .
(a) 16 m2 (b) 18m2 (c) 12m2 (d) 10m2
Solution.
Diagonal of cube = a√3
√12 = a√3
2√3 = a√3
a = 2
Lateral surface area of cube is 4a2
= 4 x (2)2
4 x 4 = 16 m2
Solution
Q3.
In a cube area of base is 4 cm2 find the total surface area of cube .
(a) 24 (b) 28 (c) 30 (d) 16
Solution.
a2 = 4
a = 2
Total surface area = 6a2
= 6(2)2
= 24 cm2
Solution
Q4.
Length of cube is 1 m, find the ratio of total surface area and lateral surface area.
(a) 6:5 (b) 4:3 (c) 2:3 (d) 3:2
Solution.
Total surface area : lateral surface area
6(1)2 : 4(1)2
6:4
3:2
Solution
Q5.
Diagonal of a cube is 3 cm its volume is ______ cm3.
(a) 2 (b) 3 (c) √3 (d) 3√3
Solution.
(d) 3√3
Solution
Q6.
A cube of sides 4 cm is melted and smaller cubes of sides 2 cm each are formed . How many such cubes are developed .
Solution.
Formula : number of cubes developed =
(
original length of side/new length of side
)
3 8
Solution
Q7.
Total surface area of a cuboid is 65 cm2 and its lateral surface area is 35cm2. find the area of its base?
(a) 18cm2 (b) 25cm2 (c) 15cm2 (d) 20cm2
Solution.
Total surface area of cuboid = 2(Area of base) + lateral surface area .
65 = 2(Area of base) + 35
Area of base = 15 cm2
Solution
Q8.
The side of cube is increase by 50% . Find the percentage increase in its volume .
Solution.
237.5%
Solution
Q9.
A cube has diagonal √3cm It volume is _________ cm3
(a) 1 (b) 2 (c) 3 (d) 4
Answer.
(a) 1
Solution
Q10.
Ratio of the lateral surface area of two cubes is 16:36. find the ratios of their sides ?
(a) 1:2 (b) 4:3 (c) 6:7 (d) 4:6
Answer.
(d) 4:6
Solution
