Question 1: Find the lateral surface area and total surface area of a cuboid of length , breadth and height .

Answer:

Dimension of cuboid: Length , Breadth and Height

Lateral surface area

Total surface area

Question 2: Find the lateral surface area and total surface area of a cube of edge .

Answer:

Dimension of the cube: Length

Lateral surface area

Total surface area

Question 3: Find the ratio of the total surface area and lateral surface area of a cube.

Answer:

Let the length of the side of the cube

Lateral surface area

Total surface area

Therefore

Question 4: Mary wants to decorate her Christmas tree. She wants to place the tree on a wooden block covered with colored paper with picture of Santa Claus on it. She must know the exact quantity of paper to buy for this purpose. If the box has length, breadth and height as , and respectively. How many square sheets of paper of side would she require?

Answer:

Dimension of box: Length , Breadth and Height

Total surface area

Therefore No of sheets sheets

Question 5: The length, breadth and height of a room are and respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of .

Answer:

Dimension of room: Length , Breadth and Height

Area to be painted Lateral surface area Roof

Painting rate

Therefore Total cost

Question 6: Three equal cubes are placed adjacently in a row. Find the ratio of total surface area of the new cuboid to that of the sum of the surface areas of the three cubes.

Answer:

Let the length of the side of the cube

Total surface area of one cube

Total surface area of three cubes

Dimension of cuboid: Length , Breadth and Height

Total surface area

Therefore

Question 7: A cube is cut into cubes. calculate the total surface area of all the small cubes.

Answer:

Dimension of big cube

Volume of Big cube

Dimension of small cube

Volume of small cube

Therefore no of small cubes $latex = 6 $

Therefore Total surface area of small cubes

Question 8: The length of a hall is and the width . The sum of the areas of the floor and the flat roof is equal to the sum of the areas of the four walls. Find the height of the hall.

Answer:

Dimension of hall: Length , Breadth and Height

Area of floor

Area of Roof

Lateral surface area of room

Hence

Question 9: Hameed has built a cubical water tank with lid for his house, with each other edge long. He gets the outer surface of the tank excluding the base covered with square tiles of side . Find how much he would spend for the tiles, if the cost of tiles is per dozen.

Answer:

Dimension of cubical tank: Length

Total surface are to be tiles = Lateral surface area + Top

Area of one square tile

Therefore the number of tiles used

Hence the total cost of the tiles

Question 10: Each edge of a cube is increased by . Find the percentage increase in the surface area of the cube.

Answer:

Let the initial dimension of the cube

Final dimension of the cube

Total surface area of initial cube

Total surface area of enlarged cube

Therefore increase in surface area

Therefore percentage increase

Question 11: The dimensions of a rectangular box are int he ratio of and the difference between the cost of covering it with sheet of paper at the rates of and is . Find the dimensions of the box.

Answer:

Let the dimension of the box: Length , Breadth and Height

Total surface area

Cost of covering with

Cost of covering with

Therefore

Hence the dimensions are: Length , Breadth and Height

Question 12: A closed iron tank long, wide and deep is to be made. Determine the cost of iron sheet used at the rate of per meter sheet, sheet being wide.

Answer:

Dimension of the Iron tank: Length , Breadth and Height

Total surface area

Therefore length of sheet required

Hence the cost of the Iron sheet

Question 13: Ravish wanted to make a temporary shelter for his car by making a box-like structure with tarpaulin that covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much. tarpaulins would be required to make the shelter of height with base dimensions ?

Answer:

Dimension of the Car park: Length , Breadth and Height

Area of trampoline Total lateral surface area Top surface area

Question 14: An open box is made of wood thick. Its external length, breadth and height are and . Find the cost of painting the inner surface of .

Answer:

Thickness of box

Dimension of the Box: Length , Breadth and Height

Height of the painted surface

Length of painted surface

Breadth of the painted surface

Therefore area to be painted

Hence cost of painting

Question 15: The cost of preparing the walls of a room long at the rate of per square meter is and the cost of matting the floor at paise per square meter is . Find the height of the room.

Answer:

Dimension of the Room: Length , Breadth and Height

Lateral surface area

Cost of preparing walls at rate of

Hence

… … … … … i)

Cost of matting the floor

Therefore substituting this in i) we get

Question 16: The dimensions of a room are . There are doors and windows in the room; each door measures and each window . Find the cost of painting the walls at per square meter.

Answer:

Dimension of the Room: Length , Breadth and Height

Number of doors

Dimension of door: Breadth and Height

Number of windows

Dimension of window: Breadth and Height

Lateral surface area of walls

Surface area of doors and windows

Therefore Area to be painted

Therefore cost of painting

Question 17: The length and breadth of a hall are in the ratio and its height is . The cost of decorating its walls (including doors and windows) at per square meter is . Find the length and breadth of the room.

Answer:

Dimension of the Room: Length , Breadth and Height

Lateral surface area

Cost of decorating

Therefore

Therefore Length , Breadth

Question 18: A wooden bookshelf has external dimensions as follows: Height , Depth , Breadth . The thickness of the plank is ever where. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is and the rate of painting . Find the total expenses required for polishing and painting the surface of the bookshelf.

Answer:

External Dimension of the book shelf: Length , Breadth and Width

Internal Dimension of the book shelf: Length , Breadth and Width

External surface are to be polished

Therefore cost of polishing

Internal surface area Area of the five faces of 3 cuboids

Cost of painting the internal surface

Hence the total cost

Question 19: The paint in a certain container is sufficient to paint on area equal to . How many bricks of dimension can be painted out of this container?

Answer:

Dimension of the brick: Length , Breadth and Width

Total surface area

Therefore the number of bricks that can be painted