**Q1. The volume of cuboid is 6 times the volume of a cube. If the dimensions of the cuboid are 9 cm, 18 cm and 48 cm. The total surface area of the cube **

(a) 6912

(b) 13824

(c) 7776

(d) 25920

**S1. Ans.(c)**

**Sol. **Volume of cube = 6 × 9 × 18 × 48

= 2 × 3 × 3 × 3 × 2 × 3 × 3 × 4 × 4 × 3

Side of the cube = 4 × 3 × 3 = 36 cm

So, surface area of the cube =6×side^2 = 6 × 36 × 36

= 7776

**Q2. If a cube maximum possible volume is cut off from a solid sphere of diameter d, then the volume of the remaining (waste) material of the sphere would be equal to: **

**Q3. A spherical steel ball was silver polished then it was cut into 4 similar pieces. What is the ratio of the polished area to the non-polished area: **

(a) 1 : 1

(b) 1 : 2

(c) 2 : 1

(d) None of these

**Q4. The height of a right prism with a square base is 15 cm. If the area of the total surfaces of the prism is 608 sq. cm, its volume is:**

(a) 910 cm3

(b) 920 cm3

(c) 960 cn3

(d) 980 cm3

**Q5. The base of a right prism is an equilateral triangle of area 173 cm^2 and the volume of the prism is 10380 cm3. The area of the lateral surface of the prism is use(√3=1.73) **

(a) 1200 cm^2

(b) 2400 cm^2

(c) 3600 cm^2

(d) 4380 cm^2

**Q6. A hemisphere bowl B1 and a hollow right circular cylinder B2 (having length equal to its radius) have the same diameter equal to the length of a side of a hollow cubical box B3. Water is filled completely in all these vessels and the volumes of filled water are v1,v2 and v3 respectively in B1,B2 and B3 then: **

(a) V1<V2<V3

(b) V2<V3<V1

(c) V3<V2<V1

(d) V3<V1<V2

**Q7. The height of a circular cylinder is increased by 6 times and base area is decreased by 1/9th times. By what factor its lateral surface area is increased?**

(a) 2

(b) 3

(c) 6

(d) 1.5

**Q8. If from a circular sheet of paper of radius 15 cm, a sector of 144° is removed and the remaining is used to make a conical surface, then the angle at the vertex will be**:

**Q9. 250 men took a dip in a water tank at a time, which is 80m × 50m. What is the rise in the water level if the average displacement of 1 man is 4 m cubic? **

(a) 22 cm

(b) 25 cm

(c) 18 cm

(d) 30 cm

**Q10. A solid is in the form of cylinder with hemispherical ends. The total height of the solid is 19 cm and the diameter of the cylinder is 7 cm. Find the total surface area of the solid. (Use = 22/7). **

(a) 398.75 cm2

(b) 418 cm2

(c) 444 cm2

(d) 412 cm2

**Q11. Water flows out at the rate of 1000m/min from a cylindrical pipe of diameter 5 mm. Find the time taken to fill a conical tank whose diameter at the surface is 40 cm and depth 24 cm. **

(a) 50 min

(b) 102.4 min

(c) 51.2 min

(d) 25.6 min

**Q12. Three equal cubes are placed adjacently in a row. Find the ratio of total surface area of the new cuboid to that of the sum of the surface areas of the three cubes.**

(a) 7 : 9

(b) 49 : 81

(c) 9 : 7

(d) 27 : 23

**Q13. If the area of the circular shell having inner and outer radii of 8 cm and 12 cm respectively is equal to the total surface area of cylinder of radius R_1 and height h, then h, in terms or R_1 will be**

**Q14. A rectangle water tank measure 15m × 6m at top and is 10 m deep. It is full of water. If water is drawn out lowering the level by 1 meter how much of water has been drawn out? **

(a) 90,000 litres

(b) 45,000 litres

(c) 80,000 litres

(d) 40,000 litres

**Q15. The length of a room floor exceeds its breadth by 20 m. The area of the floor remains unaltered when the length is decreased by 10 m but the breadth is increased by 5 m. The area of the floor (in square metres) is: **

(a) 280

(b) 325

(c) 300

(d) 420