1.) Find the volume and surface area of a cuboid 16 m long, 14 m broad and 7 m high.

**A.** 680 **B.** 712

**C.** 868 **D.** None of these

**View Answer**

**Answer**: Option **C**

**Explanation:**

Sol. Volume = (16 x 14 x 7) m3 = 1568 m3.

Surface area = [2 (16 x 14 + 14 x 7 + 16 x 7)] cm^{2}

= (2 x 434) cm^{2} = **868 cm ^{2}.**

2.) Find the length of the longest pole that can be placed in a room 12m long 8m broad and 9m high.

**A.** 12 **B.** 13

**C.** 15 **D.** 17

**View Answer**

**Answer**: Option **D**

**Explanation:**

Sol. Length of longest pole = Length of the diagonal of the room

= √(12^{2}+8^{2}+9^{2}= √(289)= **17 m.**

3.) 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?

**A.** 19680 **B.** 29650

**C.** 38161 **D.** 45000

**View Answer**

**Answer**: Option **D**

**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.

Number of bricks= (90/100)*(2400*800*60)/ (24*12*8)

**= 45000.**

4.) 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.

**A.** 20 **B.** 30

**C.** 40 **D.** 50

**View Answer**

**Answer**: Option **C**

**Explanation:**

Volume of the block = (6 x 12 x 15) cm^{3} = 1080 cm^{3}.

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) cm^{3} = 27 cm^{3}.

Number of cubes = 1080/27 = **40.**

5.) 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.

**A.** 11.25 cm **B.** 13.19 cm

**C.** 16.21 cm **D.** None of these

**View Answer**

**Answer**: Option **A**

**Explanation:**

Sol. Increase in volume = Volume of the cube = (15 x 15 x 15) cm^{3}.

Rise in water level = volume/area = (15 x 15 x 15)/ (20 x 15) cm

= **11.25 cm.**