43954.A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:
90 cm
1 dm
1 m
1.1 cm
Explanation:
Let the thickness of the bottom be x cm.
Then, [(330 - 10) x (260 - 10) x (110 - x)] = 8000 x 1000
=> 320 x 250 x (110 - x) = 8000 x 1000
=> (110 - x) = $\dfrac{8000 \times 1000}{320 \times 250} = 100$
=> x = 10 cm = 1 dm.
Let the thickness of the bottom be x cm.
Then, [(330 - 10) x (260 - 10) x (110 - x)] = 8000 x 1000
=> 320 x 250 x (110 - x) = 8000 x 1000
=> (110 - x) = $\dfrac{8000 \times 1000}{320 \times 250} = 100$
=> x = 10 cm = 1 dm.
43956.A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in $m^3$) is:
4830
5120
6420
8960
Explanation:
Clearly, l = (48 - 16)m = 32 m,
b = (36 -16)m = 20 m,
h = 8 m.
ஃ Volume of the box = (32 x 20 x 8) $m^3 = 5120 m^3.$
Clearly, l = (48 - 16)m = 32 m,
b = (36 -16)m = 20 m,
h = 8 m.
ஃ Volume of the box = (32 x 20 x 8) $m^3 = 5120 m^3.$
43959.How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?
5600
6000
6400
7200
Explanation:
Number of bricks = $\dfrac{Volume of the wall}{Volume of 1 brick}$ = $(\dfrac{800 \times 600 \times 22.5}{25 \times 11.25 \times 6})$ = 6400.
Number of bricks = $\dfrac{Volume of the wall}{Volume of 1 brick}$ = $(\dfrac{800 \times 600 \times 22.5}{25 \times 11.25 \times 6})$ = 6400.
43961.In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
75 cu. m
750 cu. m
7500 cu. m
75000 cu. m
Explanation:
1 hectare = 10,000 $m^2$
So, Area = (1.5 x 10000) m2 = 15000 m2.
Depth =$ \dfrac{5}{100}m = \dfrac{1}{20}m$
ஃVolume = (Area x Depth) = $(15000 \times \dfrac{1}{20})m^3 = 750 m^3$
1 hectare = 10,000 $m^2$
So, Area = (1.5 x 10000) m2 = 15000 m2.
Depth =$ \dfrac{5}{100}m = \dfrac{1}{20}m$
ஃVolume = (Area x Depth) = $(15000 \times \dfrac{1}{20})m^3 = 750 m^3$
43967.The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.
$30 \pi m^2$
$40 \pi m^2$
$60 \pi m^2$
$80 \pi m^2$
Explanation:
l = 10 m,
h = 8 m.
So, $r = \sqrt{l^2 - h^2} = \sqrt{(10)^2 - (8)^2} = 6m$
ஃ Curved surface area =$ \pi rl = (\pi \times 6 \times 10) m^2 = 60 \pi m^2.$
l = 10 m,
h = 8 m.
So, $r = \sqrt{l^2 - h^2} = \sqrt{(10)^2 - (8)^2} = 6m$
ஃ Curved surface area =$ \pi rl = (\pi \times 6 \times 10) m^2 = 60 \pi m^2.$
43968.A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:
12 kg
60 kg
72 kg
96 kg
Explanation:
Volume of water displaced = (3 x 2 x 0.01)$m^3$
= $0.06 m^3.$
ஃ Mass of man = Volume of water displaced x Density of water
= (0.06 x 1000) kg
= 60 kg.
Volume of water displaced = (3 x 2 x 0.01)$m^3$
= $0.06 m^3.$
ஃ Mass of man = Volume of water displaced x Density of water
= (0.06 x 1000) kg
= 60 kg.
44170.Rajat makes 8 open cones of height 24 cm and slant height 25 cm from a sheet of thick paper. Find the area of the sheet.
550 sq. m.
4400 sq. m.
6000 sq. m.
6236 sq.m.
Explanation:
L2 = r2 + h2 = 252 - 242
∴ r = 7 cm
Curved surface area of cone = 3.142 x 7 x 25 = 550 sq.m.
Since the cone is open, it means, it just has curved surface.One sheet can make 8 cones.
So area of one sheet = Curved surface area of 8 cones = 8 x 550
∴ Area of one sheet = 4400 sq.cm.
L2 = r2 + h2 = 252 - 242
∴ r = 7 cm
Curved surface area of cone = 3.142 x 7 x 25 = 550 sq.m.
Since the cone is open, it means, it just has curved surface.One sheet can make 8 cones.
So area of one sheet = Curved surface area of 8 cones = 8 x 550
∴ Area of one sheet = 4400 sq.cm.
44173.Find the number of bricks, each measuring 24 cm x 12 cm x 8 cm, required to construct a wall 24 m long, 8m high and 60 cm thick, if 10% of the wall is filled with mortar?
19680
29650
38161
45000
Explanation:
Volume of the wall = (2400 x 800 x 60) cu. cm.
Volume of bricks = 90% of the volume of the wall
= ((90/100)* 2400 * 800 * 60) cm.
Volume of 1 brick = (24 x 12 x 8) cm.
bindu Number of bricks= (90/100)*(2400*800*60)/ (24*12*8)
= 45000.
Volume of the wall = (2400 x 800 x 60) cu. cm.
Volume of bricks = 90% of the volume of the wall
= ((90/100)* 2400 * 800 * 60) cm.
Volume of 1 brick = (24 x 12 x 8) cm.
bindu Number of bricks= (90/100)*(2400*800*60)/ (24*12*8)
= 45000.
44176.A rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact number of equal cubes. Find the least possible number of cubes.
20
30
40
50
Explanation:
Volume of the block = (6 x 12 x 15) cm3 = 1080 cm3.
Side of the largest cube = H.C.F. of 6 cm, 12 cm, 15 cm = 3 cm.
Volume of this cube = (3 x 3 x 3) cm3 = 27 cm3.
Number of cubes = 1080/27 = 40.
Volume of the block = (6 x 12 x 15) cm3 = 1080 cm3.
Side of the largest cube = H.C.F. of 6 cm, 12 cm, 15 cm = 3 cm.
Volume of this cube = (3 x 3 x 3) cm3 = 27 cm3.
Number of cubes = 1080/27 = 40.
44177.A cube of edge 15 cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base of vessel are 20 cm x 15 cm, find the rise in water level.
11.25 cm
13.19 cm
16.21 cm
None of these
Explanation:
Increase in volume = Volume of the cube = (15 x 15 x 15) cm3.
binduRise in water level = volume/area = (15 x 15 x 15)/ (20 x 15) cm
= 11.25 cm.
Increase in volume = Volume of the cube = (15 x 15 x 15) cm3.
binduRise in water level = volume/area = (15 x 15 x 15)/ (20 x 15) cm
= 11.25 cm.