Mathematics - Mensuration
Exam Duration: 45 Mins Total Questions : 25
Two rectangles ABCD and DBEF are as shown in the figure. The area of rectangle DBEF (in square units) ________
- (a)
10
- (b)
12
- (c)
14
- (d)
15
The ratio of areas of two squares, if diagonal of one is double the diagonal of the other, is _____
- (a)
3 : 2
- (b)
4 : 1
- (c)
3 : 1
- (d)
4 : 3
Ratio of surface areas of two cubes is 25 : 36 Find the ratio of their volumes
- (a)
5 : 6
- (b)
125 : 216
- (c)
1 : 2
- (d)
64 : 216
The area of a quadrilateral is 342 sq.m. The perpendiculars from two of its opposite vertices to the diagonal are 12 m and 12 m. What is the length of the diagonal?
- (a)
28.6 cm
- (b)
25.3 cm
- (c)
28.5 cm
- (d)
22.5 cm
The radii of the bases of two cylinders are in the ratio of 1 : 2 respectively and their heights are in the ratio 2 : 1 respectively. Find the ratio of their volumes.
- (a)
1 : 2
- (b)
1 : 4
- (c)
2 : 1
- (d)
4 : 1
Find the sum of the lengths of the parallel sides of a trapezium whose altitude is 11 cm and whose area is 0.55 m2
- (a)
25m
- (b)
15m
- (c)
12m
- (d)
10m
In the given figure, RSTV is a square inscribed in a circle with centre O and radius r. The total area of the shaded region is ________
- (a)
r2 (π - 2)
- (b)
2r2 (2-π)
- (c)
π (r2 - 2)
- (d)
8r2 - 8r
ABC is a right angled triangle with ㄥBAC = 90°. AH is drawn perpendicular to BC. If AB = 60 cm and AC = 80 cm, then BH = ________
- (a)
36cm
- (b)
32 cm
- (c)
24 cm
- (d)
30 cm
Three cubes whose edges are 3 cm, 4 cm and 5 cm respectively are melted without any loss of metal into a single cube. The edge of the new cube is ______
- (a)
6 cm
- (b)
12 cm
- (c)
9cm
- (d)
10cm
The volume of a cuboid is 440cm3 and the area of its base is 88 cm2. Find its height
- (a)
5 cm
- (b)
11 cm
- (c)
4 cm
- (d)
8 cm
A hoop is resting vertically at staircase as shown in the diagram. AB = 12 cm and Be = 8 cm. The radius of the hoop is _________
- (a)
13cm
- (b)
12√2 cm
- (c)
14cm
- (d)
13√2 cm
The capacity of a closed cylindrical water tank is 9.24 kilolitres. If the height of the cylinder is 1.5 m, what is its radius?
- (a)
1.4 m
- (b)
14 m
- (c)
7m
- (d)
0.7 m
The thickness of a hollow metallic cylinder is 2cm. It is 70 cm long with outer radius of 14 cm. Find the volume of the metal used in making the cylinder, assuming that it is open at both the ends. Also find its weight if the metal weighs 8 g per cm3
- (a)
10440 cm3 91250 g
- (b)
13440 cm3 90000 g
- (c)
13440 cm3 90000 g
- (d)
11440 cm3, 91520 g
- (e)
12440 cm3, 91550 g
A wooden box (including the lid) has external dimensions 40 cm by 34 cm by 30 cm. If the wood is 1 cm thick, then how many cm3 of wood is used in it?
- (a)
6752 cm2
- (b)
6750 cm3
- (c)
5752 cm3
- (d)
5750 cm3
How many bricks of size 22 cm x 10 cm x 7 cm are required to construct a wall 11m long, 3.5 m high and 40 cm thick, if the cement and sand used in the construction occupy (1/10)th part of the wall?
- (a)
8000
- (b)
9000
- (c)
7000
- (d)
10000
A rectangular block of ice measures 40cm by 25 cm by 15 cm. Calculate its weight (in kg), if ice weighs \(9\over 10\) of the weight of the same volume of water and 1 cm3 of water weighs 1 gm
- (a)
9
- (b)
13.5
- (c)
8
- (d)
9.5
A cylindrical tower is 5 metres in diameter and 14 metres high. The cost of white washing its curved surface at 50 paise per m2 is ______
- (a)
Rs.90
- (b)
Rs.97
- (c)
Rs.110
- (d)
Rs.95
A square garden measuring 8 m on a side is surrounded by a 1 m wide path. What is the area of the path?
- (a)
8m2
- (b)
9m2
- (c)
28m2
- (d)
36m2
A well 12 m deep with a diameter 3.5 m is dug up and earth from it is evenly spread to form a platform 10.5 m long and 8.8 m wide. Find the height of the platform
- (a)
2.5 m
- (b)
12.5 m
- (c)
1.25 m
- (d)
1.5 m
A room is 9 m long, 6 m wide and 4 m high. Find the cost of plastering its walls and ceiling at the rate of Rs.2.50 per square metre
- (a)
Rs.435
- (b)
Rs.600
- (c)
Rs.502
- (d)
Rs.534
A solid iron rectangular block of dimensions 4.4 m, 2.6 m and 1 m is cast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find the length of the pipe.
- (a)
112.5 m
- (b)
112 m
- (c)
212 m
- (d)
312 m
Find the area of the given field. All dimensions are in m.
- (a)
9000 m2
- (b)
11700 m2
- (c)
11000 m2
- (d)
12000 m2
Fill in the blanks.
(i) The perimeter of a rectangle becomes ______ times its original perimeter, if its length and breadth are doubled.
(ii) The curved surface area of a cylinder is reduced by _____ percent if the height is half of the original height.
(iii)Opposite faces of a cuboid are ______ in area.
(iv) If the diagonal d of a quadrilateral is doubled and the heights h1 and h2 falling on d are halved, then the new area of quadrilateral is __________
- (a)
(i) (ii) (iii) (iv) 2 50 equal \({1\over2}\)(h1+h2)d - (b)
(i) (ii) (iii) (iv) 2 35 unequal \({1\over2}\)(h1+h2)d - (c)
(i) (ii) (iii) (iv) 3 40 equal (h1+h2)d - (d)
(i) (ii) (iii) (iv) 3 35 unequal (h1+h2)d
Match the figure in column I with their total surface area in column II
- (a)
P ⟶ (iii); Q ⟶ (ii); R ⟶ (iv); S ⟶ (i)
- (b)
P ⟶ (ii); Q ⟶ (iv); R ⟶ (i); S ⟶ (iii)
- (c)
P ⟶ (ii); Q ⟶ (iii); R ⟶ (i); S ⟶ (iv)
- (d)
P ⟶ (ii); Q ⟶ (iv); R ⟶ (iii); S ⟶ (i)
The area of a trapezium with equal nonparallel sides is 168 m2. If the lengths of the parallel sides are 36 m and 20 m, find the length of the non-parallel sides
- (a)
8m
- (b)
10m
- (c)
15 m
- (d)
4 m
