1.

The lateral surface area of cube is 100 sq.units. find the volume of cube?

**Answer: Option 'C'**

**Lateral surface = 4 a ^{2} = 100 sq.units
a^{2} = 25
a = 5.
Cube volume = a^{3} => 125 m^{3}**

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 = a ^{3} => (8 × 8 × 8) Cm^{3} => 512 Cm^{3}
Surface area => 6 a^{2} => (6 × 8 × 8) Cm^{2} => 384 Cm^{2}**

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 πR ^{3} : 4/3 π r^{3} = 4^{3} : 3^{3} = 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 m ^{2}**

6.

The surface area of a cube is 486 Cm^{3}. Find its volume?

**Answer: Option 'C'**

**Let each edge of the cube be a Cm.
Then 6 a ^{2} = 486 => a^{2} = 81 = 9^{2} => a = 9
Volume = a^{3} = 9^{3} Cm^{3} => 729 Cm^{3}**

7.

The side of a cube is 15 m, find it's surface area?

**Answer: Option 'A'**

**Surface area = 6 a ^{2} sq. units
6 a^{2} = 6 × 225 = 1350 m^{2}**

8.

If the radius of sphere is doubled, then its volume is increased by:

**Answer: Option 'C'**

**radius = r. Original volume = 4/3 πr ^{3}
New radius = 2r New volume = 4/3 π(2r)^{3} = (32πr^{3})/3
increase in volume = ( (32πr^{3})/3 × 3/(4πr^{3}) × 100 ) % = 700%**

9.

Two cubes of thire sides ratio 2 : 3. Find its cube volumes ratio?

**Answer: Option 'C'**

**a ^{3} : b^{3} = 2^{3} : 3^{3}**

= 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
πr ^{2}h = 1/3 πr^{2}h 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)
(πr ^{2}h)/(1/3 πr^{2}h) = (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&pir ^{2}
= 2πr(h+r)
= [2 × 22/7 × 5/2 × (60 + 5/2)] Cm^{2}
= [ 44/7 × 5/2 × ( (120 + 5)/2 ) ] Cm^{2}
= 22/7 × 5 × 125/2 Cm^{2}
= (55 × 125)/7 Cm^{2}
= 6875/7 Cm^{2}
= 982.14 Cm^{2}**

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 = a ^{3} cubic units
Surface area = 6 a^{2} sq.units
a^{3} = 6 a^{2}
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 = πr ^{2}h
Volume of the cone = 1/3 πr^{2}h
(πr^{2}h)/(1/3 πr^{2}h) = 3/1 = 3 : 1**

15.

The side of a cube is 12 m, find the lateral surface area?

**Answer: Option 'D'**

**Lateral surface = 4 a ^{2}
4 × 12^{2} = 4 × 144 => 516 m^{2}**

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 m**

18.

The radius of hemi sphere 7 m, find its volume?

**Answer: Option ''**

**Hemi-sphere volume (V) = 2/3 πr ^{3}
= 2/3 × 22/7 × 7 × 7 × 7
= (44 × 49)/3 = 616/3 = 205 1/3 m^{3} 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 m ^{2}**

20.

The side of a cube is 8 m, Find the voiume?

**Answer: Option 'C'**

**Cube Volume = a ^{3}
a^{3} = 8^{3} = 512 m^{3}**

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) = √r ^{2}+h^{2}
= √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 m ^{3}**

24.

If the volume and surface area of a sphere are numerically the same, then its radius is:?

**Answer: Option 'B'**

**4/3 πr ^{3} = 4 π r^{2} **

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**

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