Volume of Cube

Exercise 13.5

Question 1: A matchbox measures 4 cm × 2.5 cm × 1.5 cm. What will be the volume of a packet containing 12 such boxes?

Answer: Given: `l=4` cm, `b=2.5` cm and `h=1.5` cm

Volume of cuboid `=l\xx\b\xx\h`

`=4xx2.5xx1.5=15` cubic cm

Question 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 m^3 = 1000 \l`)

Answer: Given: `l=6` m, `b=5` m, `h=4.5` m

Volume of cuboid `=l\xx\b\xx\h`

`=6xx5xx4.5=135` cubic m

As 1 m³ = 1000 litre

Hence, 135 m³ = 135000 litre

Question 3: A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?

Answer: Given: `l=10` m, `b=8` m, volume = 380 cubic m, h = ?

Volume of cuboid `=l\xx\b\xx\h`

Or, `380=10xx8xxh`

Or, `h=(380)/8=4.75` m

Question 4: Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of Rs 30 per m³.

Answer: Given: `l=8` m, `b=6` m, `h=3` m

Volume of cuboid `=l\xx\b\xx\h`

`=8xx6xx3=144` cubic m

Cost = Volume × Rate

`=144xx30` = Rs. 4320

Question 5: The capacity of a 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.

Answer: Given: volume = 50000 litre = 50 cubic m, `l=2.5` m, h = 10 m, b =?

Volume of cuboid `=l\xx\b\xx\h`

Or, `50=2.5xx10xx\b`

Or, `b=(50)/(25)=2` m

Question 6: A village, having a population of 4000, requires 150 litres of water per head per day. It has a tank measuring 20 m × 15 m × 6 m. For how many days will the water of this tank last?

Answer: Given: `l=20` m, `b=15` m, `h=6` m, population of village = 4000

Water requirement per person per day = 150 litre

Hence, daily requirement of water in village `=4000xx150=600000` litre = 600 cubic m

Volume of tank `=l\xx\b\xx\h`

`=20xx15xx6=1800` cubic m

Since `(1800)/(600)=3`

Hence, one full tank will last for 3 days.

Question 7: A godown measures 40 m × 25 m × 10 m. Find the maximum number of wooden crates each measuring 1.5 m × 1.25 m × 0.5 m that can be stored in the godown.

Answer: Given: `l=40` m, `b=25` m, `h=10` m

Dimensions of wooden crate: `l=1.5` m, `b=1.25` m, `h=0.5` m

Number of crates which can fit in the godown = volume of godown ÷ volume of one crate

`=(40xx25xx10)/(1.5xx1.25xx0.5)=10666.67`

Question 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.

Answer: Given: side = 12 cm

Volume of cube = side³

`=12^3=1728` cubic cm

Volume of smaller cubes `=(1728)/8=216`

Side of smaller cube can be calculated as follows:

Side³ = 216 = 6³

Or, side = 6 cm

Question 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?

Answer: Given: `h=3` m, `b=40` m, flow of river = 2km/hr

Volume of water in 1 minute `=3xx40xx2000xx1/(60)=4000` cubic m