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1.

In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:

Answer» 1 hectare = 10,000 m2 So, Area = (1.5 x 10000) m2 = 15000 m2. Depth = 5 m = 1 m. 100 20 Volume = (Area x Depth) = 15000 x 1 m3 = 750 m3. 20 Video Explanation: https://youtu.be/dDbVuBzYop8
Discussion
2.

A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:

Answer» Volume of water displaced = (3 x 2 x 0.01) m3 = 0.06 m3. Mass of man = Volume of water displaced x Density of water = (0.06 x 1000) kg = 60 kg.
Discussion
3.

The curved surface area of a cylindrical pillar is 264 m and its volume is 924 m. Find the ratio of its diameter to its height.

Answer» r2h = 924         r = 924 x 2 = 7 m. 2rh 264 264 And, 2rh = 264         h = 264 x 7 x 1 x 1 = 6m. 22 2 7 Required ratio = 2r = 14 = 7 : 3. h 6
Discussion
4.

A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:

Answer» Let the thickness of the bottom be x cm. Then, [(330 - 10) x (260 - 10) x (110 - x)] = 8000 x 1000 320 x 250 x (110 - x) = 8000 x 1000 (110 - x) = 8000 x 1000 = 100 320 x 250 x = 10 cm = 1 dm.
Discussion
5.

What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm?

Answer» h = 14 cm, r = 7 cm. So, l = (7)2 + (14)2 = 245 = 75 cm. Total surface area = rl + r2 = 22 x 7 x 75 + 22 x 7 x 7 cm2 7 7 = [154(5 + 1)] cm2 = (154 x 3.236) cm2 = 498.35 cm2.
Discussion
6.

A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?

Answer» Volume of the large cube = (33 + 43 + 53) = 216 cm3. Let the edge of the large cube be a. So, a3 = 216         a = 6 cm. Required ratio = 6 x (32 + 42 + 52) = 50 = 25 : 18. 6 x 62 36
Discussion
7.

How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?

Answer» Number of bricks = Volume of the wall = 800 x 600 x 22.5 = 6400. Volume of 1 brick 25 x 11.25 x 6
Discussion
8.

50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m, then the rise in the water level in the tank will be:

Answer» Total volume of water displaced = (4 x 50) m3 = 200 m3. Rise in water level = 200 m 0.25 m = 25 cm. 40 x 20
Discussion
9.

The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.

Answer» l = 10 m, h = 8 m. So, r = l2 - h2 = (10)2 - 82 = 6 m. Curved surface area = rl = ( x 6 x 10) m2 = 60 m2.
Discussion
10.

A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:

Answer» Area of the wet surface = [2(lb + bh + lh) - lb] = 2(bh + lh) + lb = [2 (4 x 1.25 + 6 x 1.25) + 6 x 4] m2 = 49 m2.
Discussion
11.

A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m) is:

Answer» Clearly, l = (48 - 16)m = 32 m, b = (36 -16)m = 20 m, h = 8 m. Volume of the box = (32 x 20 x 8) m3 = 5120 m3.
Discussion
12.

A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:

Answer» Clearly, we have r = 3 cm and h = 4 cm. Volume = 1 r2h = 1 x x 32 x 4 cm3 = 12 cm3. 3 3 Video Explanation: https://youtu.be/Njsid2mVwUY
Discussion
13.

A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:

Answer» 2(15 + 12) x h = 2(15 x 12) h = 180 m = 20 m. 27 3 Volume = 15 x 12 x 20 m3 = 1200 m3. 3 Video Explanation: https://youtu.be/V8EQ1YIaH74
Discussion
14.

A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8 g/cm, then the weight of the pipe is:

Answer» External radius = 4 cm, Internal radius = 3 cm. Volume of iron = 22 x [(4)2 - (3)2] x 21 cm3 7 = 22 x 7 x 1 x 21 cm3 7 = 462 cm3. Weight of iron = (462 x 8) gm = 3696 gm = 3.696 kg.
Discussion
15.

66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:

Answer» Let the length of the wire be h. Radius = 1 mm = 1 cm. Then, 2 20 22 x 1 x 1 x h = 66. 7 20 20 h = 66 x 20 x 20 x 7 = 8400 cm = 84 m. 22
Discussion