- 1. 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}**

- 2. 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}**

- 3. 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}**

- 4. 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}**

- 5. 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**

- 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 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}**

- 8. Three cubes of sides 5 m, 4 m, and 3 m are melted to form a new cube. Find the surface of the new cube?

**Answer: Option 'C'**

**Volume of the new cube = [ 5 ^{3} + 4^{3} + 3^{3} ] Cm^{3}**

= 125 + 64 + 27 = 216 Cm^{3} => a^{3} = 216 Cm^{3}

- 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. Two cubes of their volumes in the ratio 64 : 125. The ratio of their surface area is:

**Answer: Option 'B'**

**The ratio of their surface area is
64 : 125
4 : 5**

- 11. 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}**

- 12. 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}**

- 13. 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**

- 14. The length of box 12 Cm long, 8 Cm breadth and 9Cm height. Find the length of pencil in that box?

**Answer: Option 'C'**

**Diagonal (d) = √l ^{2}+b^{2}+h^{2} **

= √12^{2}+8^{2}+9^{2}

= √144+64+81

= √289 => 17 Cm

- 15. 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**

- 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. If each edge of cube increased by 20%, the percentage increase in

**Answer: Option 'A'**

**100 × (120)/100 × (120)/100 = 144 => 44%**

- 18. How many cuboids of length 5 m, width 3 m and height 2 m can be farmed from a cuboid of 18 m length, 15 m width and 2 m height.

**Answer: Option 'D'**

**(18 × 15 × 12)/(5 × 3 × 2) = 108**

- 19. 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**

- 20. The radius of a cylinder is 10 m, height 14 m. The volume of the cylinder is:

**Answer: Option 'C'**

**Cylinder volume = πr ^{2}h
= 22/7 × 10 × 10 × 14
= 4400 m^{3}**

- 21. The radius of a cylinder is 12 m, height 21 m. the lateral surface area of the cylinder is:

**Answer: Option 'C'**

**Lateral surface area = 2πrh
= 2 × 22/7 × 12 × 21
= 44 × 36
= 1584 m**

- 22. The radius of a cylinder is 6 m, height 21 m. The total surface area of the cylinder is?

**Answer: Option 'D'**

**Total surface area of the cylinder is = 2πr (r+h)
= 2 × 22/7 × 6(6+8)
= 2 × 22/7 × 6(14) = 44 × 12 = 528 m**

- 23. 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}**

- 24. The height of cylinder is 14 Cm and its diameter is 10 Cm. The volume of the cylinder is:

**Answer: Option 'B'**

**
h = 14 Cm and r = 5 Cm
Cylinder volume = πr ^{2}h = (22/7 × 5 × 5 × 14) Cm^{3} = 1100 Cm^{3}**

- 25. Two cylinders of theis radius in the ratio 3 : 5 and heights in the ratio 10 : 9. Then find the volumes ratio?

**Answer: Option 'D'**

**πR ^{2}H : πr^{2}h **

9 × 10 : 25 × 9

90 : 225

2 : 5

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