1What is the most water a cube shaped tank of side 6 ft can hold? (\( 1 \text{ ft}^3 = 28.317 \text{ l} \))
2What is the most water a cuboid shaped tank 2 m long, 1.5 m wide and 2 m high can hold?
3What is the most water a cylindrical tank of diameter 1 m and height 4 m can hold?
4A trapezium shaped parking area ABCD has parallel sides AD = 10 ft and BC = 12 ft, 8 ft apart. Find its area, and the number of bricks of 0.222 sq. ft each needed to pave it.
5For the same parking area, a brick costs Rs. 16, and 2 workers finish in 3 days at Rs. 1200 per worker per day. What is the total cost including the bricks?
6A garden ABCD has sides AB = 10 m, BC = 11 m, CD = 15 m and DA = 14 m. Find its perimeter, and the wire needed to go round it 5 times.
7The wire for that garden costs Rs. 80 per metre, and 3 workers take 2 days at Rs. 1500 per worker per day. What is the total cost of fencing including wages?
8A cube shaped room of side 9 ft has two square windows of side 2 ft and two doors of 5 ft × 3 ft. Find the area of the floor, and of the four walls excluding the windows and doors.
9What does it cost to paint the four walls of that room, doors and windows included, at Rs. 350 per sq. ft? Another room with every measurement 1 ft greater is painted the same way at Rs. 340 per sq. ft. By how much does the cost change?
10A well needs 60 concrete rings, each 3.5 ft across and 1 ft high. A ring costs Rs. 1200, and 2 workers take 12 days to place them at Rs. 1500 per worker per day. Find the cost of the rings alone, and the total cost of the well.
11What is the most water that well can hold? (\( 1 \text{ ft}^3 = 28.317 \text{ l} \))
12In that well the water level is seen at the 35th ring, counting from the top. How much water is in the well, and how many more litres would fill it?
13Two square based pillars 10 ft high, with base side 5 ft, stand at a house gate. Each carries a pyramid of the same base and height 1 ft. Find the slant height of the pyramid and the cost of painting the pillars with their pyramids at Rs. 94 per sq. ft.
14Two square based pillars 6 ft high with base side 1 ft each carry a pyramid of the same base and height 1 ft. Give the formula for the lateral surface of a square based pyramid, find the slant height, and find the tiling rate per sq. ft if tiling both costs Rs. 2729.
15A rainwater tank in a nursery is a cylinder of inner diameter 2.80 m and height 3 m with a cone of vertical height 0.72 m on top. Give the formula for the volume of a cylinder, find the capacity, and find the cost of filling it at Rs. 1.85 per litre.
16A pyramid shaped tent is made from 8 equal triangular pieces of cloth with sides 5 m, 6 m and 6 m. Find the area of one piece, the total cloth, and the cost at Rs. 600 per square metre.
17Three paper square based pyramids each have base side 12 cm and slant height 10 cm. Find the vertical height, the space they occupy, and the cost of colouring them, excluding the bases, at Rs. 80 per cm².
18A well is built from 32 rings, each 3.5 ft across and 1 ft high, at Rs. 1200 a ring. Find the cost of the well, its volume, and the empty volume above the water when water fills it up to the 18th ring from the bottom.
19Why is the whole surface formula of a cuboid not used when a room is painted?
20A wall of 50 m² is painted at Rs. 10 per square foot. What does it cost? (\( 1 \text{ m}^2 \approx 10.764 \text{ ft}^2 \))
21When a pillar topped with a pyramid is painted, which faces are left out, and why?
22If the rate for painting the same area rises by one quarter, by what fraction does the total cost rise? For 646 sq. ft at Rs. 40 per sq. ft, how much is the rise?