Question 1. Find the volume, the total surface area and the lateral surface area of the cuboid having:

i)

ii)

Answer:

i) Volume of a cuboid

Total surface Area of a cuboid

Lateral surface Area of a cuboid

ii) Volume of a cuboid

Total surface Area of a cuboid

Lateral surface Area of a cuboid

Question 2. Find the capacity of a rectangular tub whose length , breadth and depth . Also find the area of the iron sheet required to make the tub.

Answer:

Volume of the tub

Total surface Area of a cuboid

Question 3. A wall of length , width and height is to be constructed by using bricks of dimensions . How many bricks would be needed.

Answer:

Volume of the wall

Volume of the brick

Number of bricks needed

Question 4. How many planks each measuring can be stored in a place deep?

Answer:

Volume of the place

Volume of the plank

Number of planks stored

Question 5. A classroom is height. If each student is given of the floor area, how many students can be accommodated in the room? How many cubic meters of air would each student get?

Answer:

Area of the floor of the classroom

Area given to each student

Number of students that can be accommodated in the room

Cubic meters of air would each student get

Question 6. Find the length of the longest pole that can be placed in a room broad and high.

Answer:

Diagonal of a cuboid is the longest pole that can be placed in the room

Question 7. The volume of the cuboid is . If its length and breadth be respectively, find its height.

Answer:

Volume of a cuboid

Question 8. The volume of the cuboid is . Its length is and its breadth and height Are in the ratio of . Find the breadth and height of the cube.

Answer:

Volume of a cuboid

Question 9. The surface area of the cuboid is . Its length and breadth are respectively. Find its height.

Answer:

Surface Area of a cuboid

Question 10. The length, breadth and height of the room are respectively. Find: i) the area of the four walls of the room ii)the area of the floor of the room.

Answer:

i) Area of four walls would be

ii) The area of the floor of the room

Question 11. A room high has one door and two windows each . Find the: i) area of four walls, excluding the doors and the windows. ii) cost of painting the wall from inside at a rate of . iii) the cost of painting the ceiling at .

Answer:

i) Area of walls excluding the doors are windows

ii) Cost of painting the wall

iii) Costof painting the ceiling

Question 12. An assembly hall is height. It has five doors, each measuring and four windows each. Find the

i) cost of wall paper at a rate of

ii) cost of carpeting the floor at the rate of .

Answer:

Wall dimensions:

Door dimensions

Window dimensions

Area of walls excluding the doors are windows

i) Cost of painting the wall

ii) cost of carpeting the floor

Question 13 The length, breadth and height of the cuboid are in the ratio of . If the surface area of the cuboid is , find its dimensions. Also find the volume of the cuboid.

Answer:

Wall dimensions:

Surface Area of a cuboid

Volume

Question 14. If the area of the three adjacent faces of a cuboidal box are respectively, then find the volume of the box.

Answer:

Let the dimensions:

Multiplying the above three expressions we get

Question 15. A river deep and wide is flowing at a rate of . How many cubic meters of water runs into the sea per minute?

Answer:

Rate of flow

Volume of water flowing

Question 16. A closed wooded box high, is made up of wood 2.5 \ cm thick. Find i) the capacity of the box, ii) weight of the box if of wood weighs grams.

Answer:

External Volume of the Box

Internal Length

Internal Breadth

Internal Height

Internal Volume

Volume of Wood

Question 17 The external dimensions of a wooden box, open at the top are . It is made up of wood thick. Calculate i) the capacity of the box ii) the volume of the wood.

Answer:

External Volume of the Box

Internal Length

Internal Breadth

Internal Height

Internal Volume

Volume of Wood

Question 18. The internal dimension of the closed box, made up of iron thick, are by . Find the volume of the iron in the box.

Answer:

Internal Volume of the Box

External Length

External Breadth

External Height

External Volume

Volume of Iron

Question 19. Find the volume, the total surface area and the lateral surface area and the diagonal of each cube whose edges measures: i) ii) iii)

Answer:

i) Volume of a cube

Total surface Area of a cube

Lateral surface Area of a cube

Diagonal of a cube

ii) Volume of a cube

Total surface Area of a cube

Lateral surface Area of a cube

Diagonal of a cube

iii) Volume of a cube

Total surface Area of a cube

Lateral surface Area of a cube

Diagonal of a cube

Question 20. The surface area of the cube is . Find its volume.

Answer:

Surface Area of a cube

Therefore Volume of cube

Question 21. The volume of the cube is . Find its surface area.

Answer:

Volume of a cube

Surface area

Question 22. The volume of a cube is . Find its surface area.

Answer:

Volume of a cube

Surface area

Question 23. A solid piece of metal in the form of cuboid of dimensions is melted down and re-casted into a cube. Find the length of each edge of the cube.

Answer:

Volume of a cuboid

Let the dimension of cube

Volume of Cube

Question 24. Three cubes of metal with edges are melted to form a single cube. Find the lateral surface area of the new cube formed.

Answer:

Let the dimension of the large cube

Volume of Large Cube

Therefore the dimension of the large cube

Lateral surface Area of a cube