myhelper: RD Sharma 2020 solution class 9 chapter 18 Surface Area and Volume of a Cuboid and Cube Exercise 18.1

Exercise 18.1

Page-18.14

Question 1:

Find the lateral surface area and total surface area of a cuboid of length 80 cm, breadth 40 cm and height 20 cm.

Answer 1:

Dimensions are given as

Length

Breadth

Height

We have to find lateral surface area and total area

Hence its, lateral surface area,

Total surface area,

The lateral surface area of the cuboids is and total surface area of it is.

Question 2:

Find the lateral surface area and total surface area of a cube of edge 10 cm.

Answer 2:

Edge of the given cube,

We have to find lateral and total surface area

Lateral surface area,

Total surface area,

The lateral surface area of the cube is and its total surface area is.

Question 3:

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

Answer 3:

Let the length of the edge of the cube be

We have to find the ratio of total surface area and lateral surface area

Total surface area of the cube,

Lateral surface area of the cube,

The desired ratio,

The ratio of the total surface area and the lateral surface area of a cube is.

Question 4:

Marry wants to decorate her Christmas tree.. She wants to place the tree on a wooden block covered with coloured 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 80 cm, 40 cm and 20 cm respectively. How many square sheets of paper of side 40 cm would she require?

Answer 4:

The dimensions of the cubical block are,

We are asked to find the number of square sheet paper whose side is 40 cm

Let the total surface area of the block be.

So, Mary would require in total of colored paper.

But the paper is available in square sheets of side,

Area of a single square sheet,

The number of square sheets required=

Mary would require square sheets of paper.

Question 5:

The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of Rs. 7.50 m².

Answer 5:

Dimensions of the room are,

Let,

S The total surface area to whitewash

A₁ The lateral surface area of the room

A₂ The surface area of ceiling

R The rate of whitewashing per

We know that,

We are asked to find the cost of whitewashing

Now, the total surface area to whitewash,

Total cost of whitewashing,

Hence the cost of whitewashing the room and the ceiling is .

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 surfaces areas of the three cubes.

Answer 6:

Let,

Side of each cube

Surface area of each cube

So,

Hence,

Sum of surface areas of three cubes,

The length (say l) of the newly formed cuboids is;

Its breadth (say b) and height (say h) will be the same as that of each cube.

Total surface area of the new cuboids is;

Required Ratio,

The total surface area of the new cuboids to that of the sum of the surface area of the three cubes is

Question 7:

A 4 cm cube is cut into 1 cm cubes. Calculate the total surface area of all the small cubes.

Answer 7:

We can define the following notations as follows

Side of cube

Volume of cube

Side of cube

Volume of cube

Let;

Number of cubes formed

Surface area of a single small cube

We know,

And;

The number of cubes formed,

Total surface area of all the small cubes formed

The total surface area of all the small cubes is .

Question 8:

The length of a hall is 18 m and the width 12 m. 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 8:

The hall is cubical.

Let,

Length of the cuboids

Breadth of the cuboids

Height of the cuboids

We have,

We need to find the Height of the hall

It is given that,

The sum of the areas of the floor and the flat roof is equal to the sum of the areas of the four walls

Using abbreviations, we can write the same as,

Height of the wall is .

Question 9:

Hameed has built a cubical water tank with lid for his house, with each other edge 1.5 m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm. Find how much he would spend for his tiles, if the cost of tiles is Rs 360 per dozen.

Answer 9:

The water tank is cubical.

So let,

Side of the cube

Total surface area covered by tiles

Side of each square tile

Area of each square tile

Number of tiles required

Cost of each tile

We are asked to find the total cost of the tiles

We have,

.So,

We have,

So;

Now,

The cost of tiles is per dozen.

Hence,

Total cost for the tiles

Hameed would spend for the tiles.

Question 10:

Each edge of a cube is increased by 50%. Find the percentage increase in the surface area of the cube.

Answer 10:

Let,

Initial edge of the cube

Initial surface area of the cube

Increased edge of the cube

Increased surface area of the cube

We need to find the percentage increase in the total surface area of the cube

We know that,

And

Now,

Percentage increase in

Percentage increase in the surface area of the cube is .

Question 11:

A closed iron tank 12 m long, 9 m wide and 4 m deep is to be made. Determine the cost of iron sheet used at the rate of Rs 5 per metre sheet, sheet being 2 m wide.

Answer 11:

We know,

Length of the iron tank

Width of the iron tank

Depth of the iron tank

Width of the iron sheet

Rate of the iron sheet

We need to find the cost of iron sheet used

Total surface area of the iron tank,

Length of the iron sheet required,

Cost of the required iron sheet,

The total cost of iron sheet used is .

Question 12:

Ravish wanted to make a temporary shelter for his car by making a box-like structure with tarpaulin that covers al the four sides and the top of the car (with the front face as flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height 2.5 m witt base dimensions 4 m ✕ 3 m?

Answer 12:

The shelter is a box-like structure and hence cubical.

We have,

Length of the cuboid

Breadth of the cuboid

Height of the cuboid

The total surface area of the cuboid,

The area of the base,

The quantity of tarpaulin required,

So the quantity of tarpaulin required is.

Question 13:

An open box is made of wood 3 cm thick, its external length, breadth and height are 1.48 m, 1.16 m and 8.3 dm. Find the cost of painting the inner surface of Rs 50 per sq. metre.

Answer 13:

The external dimensions of the wooden box,

Length

Breadthand height is

Thickness of the wood

We are asked to find the cost of painting

So, the internal dimensions of the box are,

Length

Breadth

Height

The internal surface area of the box,

We are given the rate of painting per square meter is

So the total cost of painting is,

The total cost of painting is .

Question 14:

The dimensions of a room are 12.5 m by 9 m by 7 m . There are 2 doors and 4 windows in the room; each door measures 2.5 m by 1.2 m and each window 1.5 m by 1 m . Find the cost of painting the walls at Rs 3.50 per square metre.

Answer 14:

We are given the dimensions of the room as l = 12.5 m, b = 9 m, h = 7 m

The lateral surface area of the room,

Surface area of each door,

Surface area of each window,

There are 2 doors and 4 windows in the room.

Hence, total area to be painted,

Rate of painting the wall at the rate of,

So, total cost of painting,

The total cost of painting is .

Question 15:

The paint in a certain container is sufficient to paint on area equal to 9.375 m². How many bricks of dimension 22.5 cm × 10 cm × 7.5 cm can be painted out of this container?

Answer 15:

The paint in the container can paint the area,

Dimensions of a single brick,

Length

Breadth

Height

We need to find the number of bricks that can be painted

Surface area of a brick,

Number of bricks that can be painted

Hencebricks can be painted out of the container.

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Question 16:

The dimensions of a rectangular box are in the ratio of 2 : 4 and the difference between the cost of covering it with sheet of paper at the rates of Rs 8 and Rs 9.50 per m² is Rs 1248. Find the dimensions of the box.

Answer 16:

The dimensions of the rectangular box are in the ratio.

So let the dimensions be,

Length

Breadth

Height

We are asked to find the dimensions of the box

The total surface area of the box,

The cost of covering it at the rate of per

We know that, the difference between above two costs is.

So,

So the dimensions of the box are;

Hence the dimensions of the box are.

Question 17:

The cost of preparing the walls of a room 12 m long at the rate of Rs 1.35 per square metre is Rs 340.20 and the cost of matting the floor at 85 paise per square metre is Rs. 91.80. Find the height of the room.

Answer 17:

We have,

Cost of matting the floor

Rate of matting per square meter

Length of the floor

Let,

Area of the floor

Width of the room

So,

Now, we have,

The cost of preparing the walls

The rate of preparing the walls

Let,

Lateral surface area of the room

Height of the room

So,

Hence, height of the room is .

Question 18:

The length and breadth of a hall are in the ratio 4 : 3 and its height is 5.5 metres. The cost of decorating its walls (including doors and windows) at Rs 6.60 per square metre is Rs 5082. Find the length and breadth of the room.

Answer 18:

The length and breadth of the hall are in the ratio 4 : 3.

Hence l = 4x, b = 3x, h = 5.5 m

Rate of decorating the wall, R = 6.6 per square meter

Total cost of decoration C = Rs.5082

We have to find the length and breadth of the room

Surface area of the walls,

Cost of decoration = A × R

Hence,

Length

Breadth

The length and breadth of the hall are and respectively.

Question 19:

A wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85 cm (See Figure). The thickness of the plank is 5 cm every where. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is 20 paise per cm² and the rate of painting is 10 paise per cm². Find the total expenses required for polishing and painting the surface of the bookshelf.