1. A matchbox measures 4 cm x 2.5 cm. x 1.5 cm. What will be the volume of a packet containing 12 such boxes ? 2. A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many litres of water can it hold? (1 m3 = 1000 l) Solution: Here, Length (l)= 6 m Breadth (b) = 5 m Depth (h) = 4.5 m ∴ Capacity = l x b x h = 6 x 5 x 4.5 m3 = 6 x 5 x (45/10) m3 = 3 x 45 = 135 m3 ∵ 1 m3 can hold 1000 l. ∴ 135 m3 can hold (135 x 1000 l = 135000 l) of water. ∴ The required amount of water in the tank = 135000 l. 3. A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of liquid? Length (l) = 10 m Breadth (b) = 8 m Volume (v) = 380 m3 Let height of the cuboid be ‘h’. Since, volume of a cuboid = l x b x h ∴ Volume of the cuboidal vessel = 10 x 8 x h m3 = 80h m3 ⇒ 80h = 380 h= 380/80 = 19/4 m = 4.75 m Thus, the required height of the liquid = 4.75 m 4. Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of ₹ 30 per m3. Solution: Length (l)= 8 m Breadth (b) = 6 m Depth (h) = 3 m ∴ Volume of the cuboidal pit = l x b x h = 8 x 6 x 3 m3 = 144 m3 Since, rate of digging the pit is ₹ 30 per m3. ∴ Cost of digging = ₹ 30 x 144 = ₹ 4320 5. The capacity of cuboidal tank is 50000 litres of water. Find the breadth of the tank, if its length and depth are respectively 2.5 m and 10 m. Length of the tank (l) = 2.5 m Depth of the tank (h) = 10 m Let breadth of the tank = b m ∴ Volume (capacity) of the tank = l x b x h = 2.5 x b x 10 m3 = (25/10) x 10 x b m3 = 25b m3 But the capacity of the tank = 50000 l = 50 m3 [∵ 1000 l = 1 m3] ∴ 25b = 50 m3 ⇒ b= (50/25) m = 2 m Thus, the depth of the tank = 2 m 6. A village, having a population of 4000, requires 150 litres of water per head per day. It has a tank measuring 20 m x 15 m x 6 m. For how many days will the water of this tank last ? 7. A godown measures 60 m x 25 m x 10 m. Find the maximum number of wooden crates each measuring 1.5 m x 1.25 m x 0.5 m that can be stored in the godown. 8. A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube ? Also, find the ratio between their surface areas. 9. A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute ?