volume and surface area / class 4-5-6 / knowledge hub

Volume / surface area of cuboid

Problem type-1

1- Find the volume,  lateral surface area and total surface area of the cuboid whose length = 22cm,  breadth = 12 CM and height = 7.5 cm

2- Find the volume,  lateral surface area and total surface area of the cuboid whose length = 15 m,  breadth = 6 m and height = 9 dm

3- Find the volume,  lateral surface area and total surface area of the cuboid whose length = 24 m,  breadth = 25cm and height = 6 m

4- Find the volume,  lateral surface area and total surface area of the cuboid whose length = 48 cm,  breadth = 6 dm and height = 1m

Problem type-2

1- Find the volume of oil in litres that can poured into a cuboidal tin whose internal dimensions are 8cm x 4cm x 10cm. 

2- The dimensions of a rectangular water tank are 2m 75cm by 1m 80cm by 1m 40cm.  How many litres of water does it hold when filled to the brim?

Hint- 1cubic meter = 1000 liter

3- A tank is 5m long,  4m wide and 3m high. How much liter of water can it hold? 

Problem type-3

1- the capacity of a cultural tank is 50,000 liters. Find the breathe of tank if it's length and depth are 2.5m and 10m respectively. 

2- The capacity of a tank is 60 kl.  If the length and breadth of the tank are 5m and 4m respectively,  then find its depth. 

Problem type-4

1- A solid rectangular piece of iron measures 1.05m x 70cm x 1.5cm . Find the weight of this piece in kilograms if 1cube CM of iron weighs 8 gram. 

Problem type-5

1- How many persons can be accommodated in a hall of length 16m breadth 12.5m and height 4.5m, assuming that3.6 cubic meter of air is required for each person? 

2- A cardboard box is 1.2m long,  72cm wide and 54cm high.  How many bars of soap can be put into it if each bar measures 6cm x 4.5cm x 4cm? 

3- How many bricks each of dimensions 18cm by 12cm by 10cm,  will be required to build a wall 12m long,  80cm thick and 3.6m high. 

4- How many bricks each 25 CM long,  10cm wide and 7.5cm thick will be required for a wall 15m long, 2.5m high and 1.25m thick.

5- How many planks of size 2m x 25cm x 8cm can be prepared from a wooden block 5m long,  70cm broad and 32cm thick.  Assuming that there is no wastage? 

6- How many bricks,  each of size 25cm x 13.5cm x 6cm,  will be required to build a wall 8m long,  5.4m high and 33cm thick? 

Problem type-6

1- A pit 5m long and 3.5m wide is dug to a certain depth. If the volume of earth taken out of it is 14 cubic meter,  What is the depth of the pit? 

Problem type-7

1 - A rectangular water tank is 90cm wide and 40cm deep.  If it contain 576 litres of water. What is its length? 

19- The rainfall recorded on a certain day was 5cm.  Find the volume of water that fell on 2 hectare field. 

20- The volume of block of gold is 0.5 cubic meter. If it is hammered into a sheet to cover an area of 1 hectare,  find the thickness of the sheet. 

21- The volume of a room is 378cubic meter.  And the area of its floor is 84 square meter. Find the height of room. 

22- a beam of wood is 5m long and 36 CM thick.  It is made of 1.35 cubic meter of wood.  What is the width of the wood? 

23- A swimming pool is 260m long and 140m wide.  If 54600 cubic meter of water is pumped into it,  find the height of the water level in it. 

24- The dimensions of a metal block are 2.25m by 1.5m by 27cm.  It is melted and recast into cubes,  each of side 45cm.  How many cubes are formed. 

Volume / surface area of cube

 

1- Find the volume,  lateral surface area and total surface area of cube each of whose edges measures 7 m

2- Find the volume,  lateral surface area and total surface area of cube each of whose edges measures 5.6 cm

3- Find the volume,  lateral surface area and total surface area of cube each of whose edges measures 8 dm 5 cm

4- find the volume of cube,  whose volume is four times the volume of a cuboid of dimensions are 8cm x 6cm x 5cm.

5-  find the volume of cube,  whose volume is four times the volume of a cuboid of dimensions are 15cm x 12cm x 10cm.

6- find the volume of cuboid,  whose volume is six times the volume of a cube,  whose each edge is 12cm.

7-  find the volume of cuboid,  whose volume is six times the volume of a cube,  whose each edge is 10cm.

8- How many boxes can be accommodated in a cubic godown of length 17m if each box requires 3.4 cubic meter of space? The boxes are placed in the room without leaving any space between them. 

9- A cuboid measures 36m by 24m by 18m.  How many cubes of edge 6m can be cut from the cuboid? 

10- A cubical block of gold was melted and cast into 10 smaller cubes of edge 1.5cm. What was the volume of the cubical block of gold? 

11- A cuboidal tank is 30cm long,  30cm wide and 1m 60 CM high.  It has water up to a height of 40cm.  How much more cubic CM of water can the tank contain? 

12- A cuboid measures 48m by32m by 24m and each edge of a cube measures 16m.  Find the ratio of their volume. 

13- The volume of cube is 729 cubic CM.  find the surface area? 

14- Find the total surface area of the cube whose volume is 343 cubic CM. 

15- the surface area of cube is 1176 square CM,  find the volume. 

16- find the volume of the cube whose total surface area is 486 square CM. 

17- A solid cubical of fine wood costs Ra 256 at Ra 500 per cubic meter. Find its volume and the length of its side. 



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