1.
The lateral surface area of cube is 100 sq.units. find the volume of cube?
Answer: Option 'C'
Lateral surface = 4 a2 = 100 sq.units
a2 = 25
a = 5.
Cube volume = a3 => 125 m3
2.
The diagonal of a cube is 8√3. find its volume and surface area.
Answer: Option 'D'
√3.a = 8 √3 => a = 8
Volume = a3 => (8 × 8 × 8) Cm3 => 512 Cm3
Surface area => 6 a2 => (6 × 8 × 8) Cm2 => 384 Cm2
3.
How many box's of length 40 Cm, width 30 Cm and height 10 Cm can be formed from a box of 6 m length, 4 m width and 2 m height.
Answer: Option 'C'
(600×400×200)/(40×30×10) = 4000
4.
Two spheres of their radious in the ratio 4 : 3. Find its volumes ratio?
Answer: Option 'C'
Sphere volume (V) = 4/3 πR3 : 4/3 π r3 = 43 : 33 = 64 : 27
5.
The radius ofa cone is 14 m, slant height is 20 m. Find the curved surface area?
Answer: Option 'D'
Cone curved surface area = πrl
22/7 × 14 × 120 = 44 × 20 = 880 m2
6.
The surface area of a cube is 486 Cm3. Find its volume?
Answer: Option 'C'
Let each edge of the cube be a Cm.
Then 6 a2 = 486 => a2 = 81 = 92 => a = 9
Volume = a3 = 93 Cm3 => 729 Cm3
7.
The side of a cube is 15 m, find it's surface area?
Answer: Option 'A'
Surface area = 6 a2 sq. units
6 a2 = 6 × 225 = 1350 m2
8.
If the radius of sphere is doubled, then its volume is increased by:
Answer: Option 'C'
radius = r. Original volume = 4/3 πr3
New radius = 2r New volume = 4/3 π(2r)3 = (32πr3)/3
increase in volume = ( (32πr3)/3 × 3/(4πr3) × 100 ) % = 700%
9.
Two cubes of thire sides ratio 2 : 3. Find its cube volumes ratio?
Answer: Option 'C'
a3 : b3 = 23 : 33
= 8 : 27
10.
The radius of the cylinder and cone are equal. find its volumes ratio:
Answer: Option 'B'
radius of the cylinder = radius of the cone
πr2h = 1/3 πr2h 1 : 1/3
3 : 1
11.
How many cones of radius 4 m, height 2 m can be formed from a cylinder of 12 m radius, 10 m height:
Answer: Option 'C'
(Cylinder volume)/(Cone volume)
(πr2h)/(1/3 πr2h) = (π × 12 × 12 × 10)/(1/3 π × 4 × 4 × 2) = 135
12.
The height of a cylinder is 60 Cm and the diameter of its base is 5 Cm. The total surface area of the cylinder is :
Answer: Option 'C'
Given h = 60 Cm and r = 5/2 Cm
Total surface area = 2πrh + 2&pir2
= 2πr(h+r)
= [2 × 22/7 × 5/2 × (60 + 5/2)] Cm2
= [ 44/7 × 5/2 × ( (120 + 5)/2 ) ] Cm2
= 22/7 × 5 × 125/2 Cm2
= (55 × 125)/7 Cm2
= 6875/7 Cm2
= 982.14 Cm2
13.
The volume of cube is equal to the surface area of that cube. Then find the distance of side of the cube?
Answer: Option 'A'
Cube volume = a3 cubic units
Surface area = 6 a2 sq.units
a3 = 6 a2
a = 6 m
14.
A cylinder and a cone have the same height and same radius of base. The ratio between the volumes of the cylinder and the cone is:
Answer: Option 'A'
Volume of the cylinder = πr2h
Volume of the cone = 1/3 πr2h
(πr2h)/(1/3 πr2h) = 3/1 = 3 : 1
15.
The side of a cube is 12 m, find the lateral surface area?
Answer: Option 'D'
Lateral surface = 4 a2
4 × 122 = 4 × 144 => 516 m2
16.
If each edge of cube increased by 10%, the percentage increase in surface area is:
Answer: Option 'A'
100 × (110)/100 × (110)/100 × (110)/100 => 1331/100 = 33.1%
17.
The total surface area of a cuboid length 12 m, breadth 10 m and height 8 m.
Answer: Option 'B'
Total surface area of cuboid
= 2 (lb+bh+lh)
= 2 (120 + 80+ 96)
= 2 (296) => 596 m2
18.
The radius of hemi sphere 7 m, find its volume?
Answer: Option ''
Hemi-sphere volume (V) = 2/3 πr3
= 2/3 × 22/7 × 7 × 7 × 7
= (44 × 49)/3 = 616/3 = 205 1/3 m3 cubic units
19.
The lateeral surface area of cuboid length 12 m, breadth 8 m and height 6m.
Answer: Option 'D'
Cuboid lateral surface = 2h(l+b)
= 2 × 6 (20) = 240 m2
20.
The side of a cube is 8 m, Find the voiume?
Answer: Option 'C'
Cube Volume = a3
a3 = 83 = 512 m3
21.
The radius of a cone is 8 m, height 6 m. Find the slant height?
Answer: Option 'B'
Answer: Option 'B'
Cone slant height (l) = √r2+h2
= √64+36 = 10 m.
22.
If each edge of cube increased by 20%, the percentage increase in
Answer: Option 'A'
100 × (120)/100 × (120)/100 = 144 => 44%
23.
Find the volume of cuboid 15 m length, 9 m breadth and 2 m height.
Answer: Option 'D'
Cuboid volume => l × b × h => 15 × 12 × 8 = 1440 m3
24.
If the volume and surface area of a sphere are numerically the same, then its radius is:?
Answer: Option 'B'
4/3 πr3 = 4 π r2
r = 3
25.
How many cubes of 10 Cm edge can be put in a cubic box of 1 m edge?
Answer: Option 'D'
(110×100×100)/10×10×10 = 1000