Home   »   Maths Questions (Mensuration) for CTET Exam...

# Maths Questions (Mensuration) for CTET Exam 2017

Q1. If the side of a cube is increased by 50%, find by what percentage the surface area of the cube is increased?
(a) 115%
(b) 500%
(c) 125%
(d) 250%
Q2. A banquet hall has the dimensions 30 m × 12 m × 5 m. Each person should get 8 m^3 of space. Find the number of persons who can be accommodated in this hall.
(a) 225
(b) 275
(c) 250
(d) 310
Q3. The ratio between the curved surface area and the total surface area of cylinder is 2: 3 and the total surface is 924 cm^2. What is the volume of the cylinder?
(a) 2156 cm^3
(b) 2566 cm^3
(c) 3592 cm^3
(d) 4526 cm3
Q4. If the curved surface area of a cylinder is 1320 cm^2 and its base radius is 21 cm, then what is its total surface area?
(a) 4512 cm^2
(b) 4092 cm^2
(c) 6304 cm^2
(d) 5482 cm^2
Q5. A spherical metal ball of 6 cm radius is melted and recast into three spherical balls. The radii of two of these balls are 3 cm and 4 cm. What is the radius of the third ball?
(a) 3.5 cm
(b) 4 cm
(c) 5 cm
(d) 7 cm
Q6. If the diagonals of a rhombus are 10 cm and 24 cm respectively, then find its perimeter.
(a) 48 cm
(b) 50 cm
(c) 52 cm
(d) 60 cm

Q8. A cylinder circumscribes a sphere. The ratio of their volume is
(a) 2 : 5
(b) 3 : 2
(c) 5 : 3
(d) 7 : 3

Q10. The perimeter of a triangle is 32 cm and the inradius of the triangle is 3.5 cm. What is the area of the triangle?
(a) 64 cm2
(b) 56 cm2
(c) 86 cm2
(d) 75 cm2
Solutions
S1. Ans.(c)
Sol. Surface area of a cube = 6a^2
Side ↑ 50%
% change in surface area = 50 + 50 + ((50 × 50)/100)
= 125%
S2. Ans.(a)
Sol. Volume of hall
= 30 × 12 × 5 m^3
Volume of a person = 8 m^3
Number of person accommodated = (30 × 12 × 5)/8
= 225
S3. Ans.(a)
Sol. Given,
(C.S.A)/(T.S.A)=2/3
C.S.A = 2/3 (T.S.A)
= 2/3 (924)
= 616 cm^2
We know,
T.S.A – C.S.A = 2 area of base
924 – 616 = 2 (πr^2 )
(308/2)=πr^2
πr^2=154 cm^2
r = 7 cm
Now, Curved Surface Area,
2πrh = 616
Here we get, h = 14
Volume = πr^2 h
=(22/7)×7×7×14
= 2156 cm^3
S4. Ans.(b)
Sol. Given, C.S.A cylinder = 1320
r = 21
2 × π × r × h = 1320
2 × (22/7) × 21 × h = 1320
h = 10
Now, T.S.A = 2πr(h + r)
= 4092 cm^2

S10. Ans.(b)
Area of a triangle = r * s
(r is the inradius and s is the semi perimeter of the triangle)
Area of triangle = 3.5 * 32/2 = 56 cm^2