Unit-7: Mensuration
(a) Surface area and volume of cube and cuboid
(b) Surface area and volume of cylinder and cone
(c) Surface area and volume of sphere
Q1.
A side of a cube is √3 cm. Find its diagonal.
(a) 2 (b) 3 (c) 4 (d) 5
Solution.
Diagonal of cube = a√3
= √3 x √3 = 3
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.
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
Q4.
Edges of a cuboid 2,3 and 5 M, find the maximum length of a rod which can be placed in side the cuboid.
(a) √38 (b) √40 (c) √50 (d) √72
Solution.
Diagonal of a cuboid is a maximum length which can be stored.
= √l2 + b2 + h2
= √(2)2 + (3)2 + (5)2
= √4 + 9 + 25
= √38
Solution
Q5.
Curved surface area of a right circular cylinder is 1100 cm2.If the circumference of the base is 110 cm, find the height of the cylinder
.
(a) 12 cm (b) 25 cm (c) 10 cm (d) 20 cm
Solution.
2πrh = 1100
Circumference (2πr) = 110
110(h) = 1100
h = 10
Solution
Q6.
For the same height and base radius, volume of cylinder will __________ times, the volume of cone.
(a) 2 (b) 1
(c) 4 (d) 3
Solution.
(d) 3
Volume of cylinder = πr2h
Volume of cone = 1/3 πr2h
Solution
Q7.
Find the volume of a cone having radius of the base as 30 cm and its slant height as 50 cm
(use π = 3.14)
(a) 49160 cm3 (b) 9980 cm3 (c) 1100 cm3 (d) 37680cm3
Solution.
r = 30 cm
l = 50 cm
h = √l2 - r2 = 40 cm
Volume of cone is = 1/3πr2h
= 37680cm3
Solution
Q8.
Height of cylinder is doubled then the new volume will be .
(a) same (b) triple (c) double (d) none of these
Solution.
(c) double
volume is πr2h
new volume = πr2(2h) = 2πr2
Solution
Q9.
Height of cylinder is (1/4)th of the original height and radius become doubled, then the volume of new cylinder will be.
(a) same (b) triple (c) double (d) none of these
Solution.
(a) same
original volume = πr2h
new volume will be = π(2r)2 x h/4
= πr2h
Solution
Q10.
A student has rectangular sheet of dimensions 22 cm x 30 cm . He want to make a cylinder in such a way so that volume is minimum. Then height of the
cylinder will be
(a) 22 cm (b) 30 cm (c) 11 cm (d) 15 cm
Solution.
(b) 30 cm
Volume will be minimum , when rectangular sheet is rolled along minimum length.
Solution
