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