RD SHARMA SOLUTION CHAPTER -18 Surface Area and Volume of a Cuboid and Cube| CLASS 9TH MATHEMATICS-EDUGROWN

Chapter 18 – Surface Areas and Volume of a Cuboid and Cube Exercise Ex. 18.1

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4Mary 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?

Solution 4

Question 5

Solution 5

Question 6Three 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.Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9Hameed has built a cubical water tank with lid for his house, with each outer 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 the titles, if the cost of tiles is Rs. 360 per dozen.Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

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 tarpaulin would be required to make the shelter of height 2.5 m, with base dimensions 4 m x 3m?Solution 12Length of shelter = 4 m
Breadth of shelter = 3 m
Height of shelter = 2.5 m

The tarpaulin will be required for top and four sides of the shelter.
Area of Tarpaulin required = 2(lh + bh) + lb
= [2(4  2.5 + 3  2.5) + 4  3] m²
= [2(10 + 7.5) + 12] m²
= 47 m²

Question 13

An open box is made of wood 3 cm thick. Its external length, breadth and height are 1.48m, 1.16 m and 8.3 dm. Find the cost of painting the inner surface at Rs 50 per sq meter.Solution 13

Question 14

Solution 14

Question 15The paint in a certain container is sufficient to paint an area equal to 9.375 m². How many bricks of dimensions 22.5 cm × 10 cm × 7.5 cm can be painted out of this container?Solution 15Total surface area of one brick = 2(lb + bh + lh)
 = [2(22.5 × 10 + 10 × 7.5 + 22.5 × 7.5)]cm²
 = 2(225 + 75 + 168.75) 
          = (2 × 468.75) cm²
 = 937.5 cm²
Let n number of bricks be painted by the container.
Area of n bricks = 937.5n cm²
Area that can be painted by the container = 9.375 m² = 93750 cm²
 93750 = 937.5n
n = 100
Thus, 100 bricks can be painted out by the container.

Question 16

Solution 16

Question 17

The cost of preparing the walls of a room 12 m long at the rate of Rs 1.35 per square meter is Rs 340.20 and the cost of matting the floor at 85 paise per square meter is Rs 91.80. Find the height of the room.Solution 17

Question 18

Solution 18

Question 19A wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85 cm. The thickness of the plank is 5 cm everywhere. 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. 

                                           Solution 19    External length (l) of bookshelf = 85 cm
    External breadth (b) of bookshelf = 25 cm
    External height (h) of bookshelf = 110 cm
    External surface area of shelf while leaving front face of shelf
                                                  = lh + 2 (lb + bh)
                                                  = [85  110 + 2 (85  25 + 25  110)] cm²
                                                  = 19100 cm²
    Area of front face = [85  110 – 75  100 + 2 (75  5)] cm²
                                                  = 1850 + 750 cm²
                                                  = 2600 cm²
    Area to be polished = (19100 + 2600) cm² = 21700 cm²
    Cost of polishing 1 cm² area = Rs 0.20
    Cost of polishing 21700 cm² area = Rs (21700  0.20) = Rs 4340    

    Now, length (l), breadth (b) height (h) of each row of bookshelf is 75 cm, 20 cm, and    30cm  respectively.
    Area to be painted in 1 row = 2 (l + h) b + lh
                                           = [2 (75 + 30)  20 + 75  30] cm²
                                           = (4200 + 2250) cm²
                                           = 6450 cm²
    Area to be painted in 3 rows = (3  6450) cm² = 19350 cm²
    Cost of painting 1 cm² area = Rs 0.10
    Cost of painting 19350 cm² area = Rs (19350  0.10) = Rs 1935    
    Total expense required for polishing and painting the surface of the bookshelf                                             = Rs(4340 + 1935) = Rs 6275

Chapter 18 – Surface Areas and Volume of a Cuboid and Cube Exercise Ex. 18.2

Question 1A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How, many litres of water can it holds? Solution 1Volume of tank = l  b  h = (6  5  4.5) m³ = 135 m³  It is given that:
 1 m³ = 1000 litres


 Thus, the tank can hold 135000 litres of water.

Question 2A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?   Solution 2Let height of cuboidal vessel be h.
Length (l) of vessel = 10 m
Width (b) of vessel = 8 m
Volume of vessel = 380 m³
l  b  h = 380        
 10  8  h = 380
 h = 4.75

 Thus, the height of the vessel should be 4.75 m.    

Question 3Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of Rs 30 per m³.

Solution 3Length (l) of the cuboidal pit = 8 m
Width (b) of the cuboidal pit = 6 m
 Depth (h) of the cuboidal pit = 3 m
Volume of the cuboidal pit = l  b  h = (8  6  3)  = 144 m³
Cost of digging 1 m³ = Rs 30
Cost of digging 144 m³ = Rs (144 30) = Rs 4320

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16A village, having a population of 4000, requires 150 litres of water per head per day. It has a tank measuring 20 m × 15 m × 6 m. For how many days will the water of this tank last?Solution 16Length (l) of the cuboidal tank = 20 m
Breadth (b) of the cuboidal tank = 15 m
Height (h) of the cuboidal tank = 6 m

Capacity of tank = l × b × h    = (20 × 15 × 6) m³ = 1800 m³ = 1800000 litres

Water consumed by people of village in 1 day = 4000 × 150 litres = 600000 litres

Let water of this tank lasts for n days.
Water consumed by all people of village in n days = capacity of tank
n × 600000 = 1800000
n = 3    
Thus, the water of tank will last for 3 days.

Question 17

A child playing with building blocks, which are of the shape of the cubes, has built a structure as shown in fig. If the edge of each cube is 3 cm, find the volume of the structure built by the child

Solution 17

Question 18A godown measures 40 m  25 m  10 m. Find the maximum number of wooden crates each measuring 1.5 m  1.25 m  0.5 m that can be stored in the godown.    

Solution 18Length  of the godown = 40 m
    Breadth  of the godown = 25 m
    Height  of the godown = 10 m

Volume of godown = l₁ b₁ h₁ = (40  25  10)  = 10000 

    Length  of a wooden crate = 1.5 m
    Breadth  of a wooden crate = 1.25 m
    Height  of a wooden crate = 0.5 m

Volume of a wooden crate =  = (1.5  1.25  0.5) m3 = 0.9375 

Let n wooden crates be stored in the godown.
Volume of n wooden crates = volume of godown
0.9375  n = 10000

Thus, 10666 wooden crates can be stored in godown.

Question 19

A wall of length 10 m was to be built across an open ground. The height of the wall is 4 m and thickness of the wall is 24 cm. If this wall is to be built up with bricks whose dimensions are 24 cm x 12 cm x 8 cm, how many bricks would be required?Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?Solution 22Rate of water flow = 2 km per hour  
Depth (h) of river = 3 m
Width (b) of river = 40 m
Volume of water flowed in 1 min 
Thus, in 1 minute 4000  = 4000000 litres of water will fall into the sea.    

Question 23

Solution 23

Question 24

Solution 24

Question 25

Solution 25

Question 26

A rectangular container, whose base is a square of side 5 cm, stands on a horizontal table, and holds water upto 1 cm from the top. When a cube is placed in the water it is completely submerged, the water rises to the top and 2 cubic cm of water overflows. Calculate the volume of the cube and also the length of its edge.Solution 26

Question 27

Solution 27

Question 28

Solution 28