# Selina Solutions Concise Maths Class 8 Chapter 21: Surface Area, Volume and Capacity

Selina Solutions Concise Maths Class 8 Chapter 21 Surface Area, Volume and Capacity consists of accurate answers to the problems present in the textbook. Each and every problem is solved with utmost care with the aim of helping students to ace their exams without fear. To get a better hold on the concepts covered in this chapter, students can access the ICSE Selina Solutions Class 8 Maths Chapter 21 Surface Area, Volume and Capacity free PDF, from the link which is given below.

This chapter has the concepts explained in a comprehensive manner to make learning fun for the students. It is highly recommended for the Class 8 students to solve the questions present in the textbook using the solutions for a better understanding of the concepts. It will also help the students with their analytical and logical thinking abilities, which is necessary to perform well in the annual exam.

## Access Selina Solutions Concise Maths Class 8 Chapter 21: Surface Area, Volume and Capacity

Exercise

Question 1.Â

Find the volume and the total surface area of a cuboid, whose:

(i) LengthÂ = 15cm, breadthÂ = 10cmÂ and heightÂ = 8cm.

Solution:-

We know that

(ii)Â l = 3.5m, b = 2.6mÂ andÂ h = 90cm,

Solution:-

QuestionÂ 2.

(ii) The volume of a cuboid is 7.68Â m3. If its length = 3.2m and height =1.0m; find its breadth.

Solution:-

Â Volume of a cuboid =7.68Â m3

Length of a cuboidÂ =3.2 m

Height of a cuboidÂ =1.0 m

Here

LengthÂ xÂ BreadthÂ xÂ HeightÂ =Â Volume of a cuboid

Substituting the values

By further calculation

(iii) The breadth and height of a rectangular solid are 1.20 m and 80 cm respectively. If the volume of the cuboid is 1.92Â m3; find its length.

Solution:-

Volume of a rectangular solid =1.92Â m3

Breadth of a rectangular solid =Â 1.20 m

Height of a rectangular solidÂ =80 cm=0.8 m

Here

LengthÂ Ã—Â BreadthÂ Ã—Â HeightÂ =Â Volume of a rectangular solid (cubical)

Substituting the values

LengthÂ Ã— 1.20 Ã— 0.8 = 1.92

By further calculation

LengthÂ Ã— 0.96 = 1.92

Question 3.

The length, breadth and height of a cuboid are in the ratioÂ 5:3:2.Â If its volume isÂ 240cm3, find its dimensions. (Dimensions means: its length, breadth and height). Also find the total surface area of theÂ cuboid.

Solution:-

Consider length of the given cuboidÂ =5x

Breadth of the given cuboidÂ =3x

Height of the given cuboidÂ =2x

We know that

Volume of the given cuboidÂ =Â LengthÂ Ã—Â BreadthÂ Ã—height

Substituting the values

=5xÃ—3xÃ—2x=30x3

It is given that

VolumeÂ =240cm3

Substituting the values

30x3=240cm3

By further calculation

Here

Length of the given cubeÂ =5x=5Ã—2=10cm

Breadth of the given cubeÂ =3x=3Ã—2=6cm

Height of the given cubeÂ =2x=2Ã—2=4cm

We know that

Total surface area of the given cuboidÂ =2(1Ã—b+bÃ—h+hÃ—1)

Substituting the values

=2(10Ã—6+6Ã—4+4Ã—10)=2(60+24+40)=2Ã—124=248cm2

QuestionÂ 4.

The length, breadth and height of a cuboid are in the ratioÂ 6:5:3.Â If its total surface area is 504 cÂ m2;Â find its dimensions. Also, find the volume of the cuboid.

Solution:-

Consider length of the cuboidÂ =6x

Height of the cuboidÂ =3x

We know that

Total surface area of the given cuboidÂ =2(1Ã—b+bÃ—h+hÃ—l)

Substituting the values

x=2 cm

Here

Length of the cuboidÂ =6x=6Ã—2=12cm

Height of the cuboidÂ =3x=3Ã—2=6cm

We get

Volume of the cuboidÂ =lÃ—bÃ—h=12Ã—10Ã—6=720cm3

QuestionÂ 5.

Find the volume and total surface area of a cube whose edge is:

(i)Â 8 cm

Solution:-

Edge of the given cube =8cm

We know that

(ii)Â 2m 40 cm.

Solution:-

(ii)Edge of the given cube =2 m 40 cm=2.40 m

We know that

QuestionÂ 6.

Find the length of each edge of a cube, if its volume is:

QuestionÂ 7.

The total surface area of a cube isÂ 216 cm2.Â Find its volume.

Solution:-

QuestionÂ 8.

A solid cuboid of metal has dimensionsÂ 24 cm, 18 cmÂ andÂ 4 cm.Â Find its volume.

Solution:-

It is given that

Length of the cuboidÂ =24 cm

Breadth of the cuboidÂ =18 cm

Height of the cuboidÂ =4 cm

We know that

Question 9.Â

A wallÂ 9 mÂ long,Â 6 mÂ high andÂ 20 cmÂ thick, is to be constructed using bricks of dimensionsÂ 30 cm, 15 cmÂ andÂ 10 cm.Â How many bricks will be required?

Â Solution:

It is given that

Length of the wallÂ =9m=9Ã—100cm=900cm

Height of the wallÂ =6m=6Ã—100cm=600cm

Breadth of the wallÂ =20 cm

We know that

QuestionÂ 10.Â

A solid cube of edgeÂ 14 cmÂ is melted down and recasted into smaller and equal cubes each of edgeÂ 2 cm;Â find the number of smaller cubes obtained.

Solution:-

We know that

Edge of the big solid cube = 14 cm

Question 11.

A closed box is cuboid in shape with length =40cm, breadth =30cm and height =50cm. It is made of thin metal sheet. Find the cost of metal sheet required to make 20 such boxes, if 1Â m2Â of metal sheet costs Rs. 45.

Solution:-

It is given that

Length of closed box (1) =40cm

And height (h) =50cm

We know that

Total surface areaÂ =2(lÃ—b+bÃ—h+hÃ—l)

Substituting the values

Question 12.

Four cubes, each of edge 9 cm, are joined as shown below:

Write the dimensions of the resulting cuboid obtained. Also, find the total surface area and the volume of the resulting cuboid.

Solution:-

Edge of each cube =9cm

(i) We know that

Length of the cuboid formed by 4 cubes (1)Â =9Ã—4=36cm

Breadth (b) =9cm and height (h) = 9cm

(ii) Total surface area of the cuboid = 2(lb + bh + hl)

Substituting the values

Question 13.

How many persons can be accommodated in a big-hall of dimensions 40 m, 25m and 15m; assuming that each person requiresÂ 5m3Â of air?

Solution:-

Question 14.

The dimension of a class-room are; length = 15m, breadth =12m and height =7.5m. Find, how many children can be accommodated in this class-room; assuming 3.6Â m3Â of air is needed for each child.

Solution:-

It is given that

Length of the room =15m

Height of the room =7.5m

We know that

Question 15.

The length, breadth and height of a room are 6m, 5.4m and 4 m respectively. Find the area of:

(i) Its four-walls

(ii) Its roof.

Solution:-

It is given that

Length of the room = 6m

Breadth of the room = 5.4m

Height of the room = 4m