Mensuration| NCERT Solutions| Class 8

NCERT Solutions of  Chapter: Mensuration. NCERT Solutions along with worksheets and notes for Class 8.

Exercise 11.1

(1) A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?

Diagram of Question 1 of Exercise 11.1 of NCERT Chapter Mensuration

(2) Mrs. Kaushik has a square plot with the measurement as shown in the figure. She wants to construct a house in the middle of the plot. A garden is developed around the house. Find the total cost of developing a garden around the house at the rate of Rs 55 per m2.

 

Diagram of Question 2 of Exercise 11.1 of Chapter Mensuration

Diagram of Question 3 of Exercise 11.1 of NCERT Chapter Mensuration

(5) An ant is moving around a few food pieces of different shapes scattered on the floor. For which food-piece would the ant have to take a longer round? Remember, circumference of a circle can be obtained by using the expression c =2  r, where r is the radius of the circle.

 

Diagram of Question 5(a) of Exercise 11.1 of NCERT Chapter Mensuration        Diagram of Question 5(b) of Exercise 11.1 of NCERT Chapter MensurationDiagram of Question 5(c) of Exercise 11.1 of NCERT Chapter Mensuration

a                                            b                                                       c

Exercise 11.2

(1) The shape of the top surface of a table is a trapezium. Find its area if its parallel sides are 1 m and 1.2 m and perpendicular distance between them is 0.8 m.

 

Diagram of Question 1 of Exercise 11.2 of NCERT Chapter Mensuration

(2) The area of a trapezium is 34 cm2 and the length of one of the parallel sides is 10 cm and its height is 4 cm. Find the length of the other parallel side.

Ans-

 

Diagram of Question 2 of Exercise 11.2 of NCERT Chapter Mensuration

(3) Length of the fence of a trapezium shaped field ABCD is 120m.If BC = 48 m, CD = 17m and AD = 40 m, find the area of tis field. Side AB is perpendicular to the parallel sides AD and BC.

Diagram of Question 3 of Exercise 11.2 of NCERT Chapter Mensuration

Ans-

(4) The diagonal of a quadrilateral shaped field is 24 m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13 m. Find the area of the field.

Diagram of Question 4 of Exercise 11.2 of NCERT Chapter Mensuration

(6) Find the area of a rhombus whose side is 6 cm and whose altitude is 4 cm. If one of its diagonals is 8 cm long. Find the length of the other diagonal.

(8) Mohan wants to buy a trapezium shaped field. Its side along the river is parallel to and twice the side along the road. If the area of this field is 10500 m2 and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.

 

Diagram of Question 8 of Exercise 11.2 of NCERT Chapter Mensuration

Ans-

Given

Let side of field along the river = a m

Let side of field along the road = b m

Side of field along the river = 2 × side of field along the road

a = 2b (condition)

Area of the trapezium field = 10500 m2

Perpendicular distance between the two parallel h = 100m

(9) Top surface of a raised platform is in the shape of a regular octagon as shown in the figure. Find the area of the octagonal surface.

 

Diagram of Question 9 of Exercise 11.2 of NCERT Chapter Mensuration

Ans-

 

(10) There is a pentagonal shaped park as shown in the figure. For finding its area Joyti and Kavita divided it in two different ways.

Find the area of this park using both ways. Can you suggest some other way of finding its area?

 

Diagram of Question 10 of Exercise 11.2 of NCERT Chapter Mensuration                                           

Ans-

Joyti’s method

Mensuration,A 10, exercise 11.2,NCERT, class 8

Kavita’s method

Mensuration,A 10, exercise 11.2,NCERT,class8

(11) Diagram of the given frame has outer dimensions = 24 × 28 cm and inner dimensions 16 × 20 cm. Find the area of each section of the frame, if the width of each section is same.

 

Diagram of Question 11 of NCERT Chapter Mensuration

Ans-

 

Exercise 11.3

(1) There are two cuboidal boxes as shown in the adjoining figure. Which box requires the lesser amount of material to make?

 

Diagram of Question 1(a) of Exercise 11.3 of NCERT Chapter Mensuration     Diagram of Question 1(b) of Exercise 11.3 of NCERT Chapter Mensuration

a                                                                     b

(4) Rukhsar painted the outside of the cabinet of measure 1 m × 2 m × 1. 5 m.

How much surface area did she cover if she painted all except the bottom of the cabinet.

 

Diagram of Question 4 of Exercise 11.3 of NCERT Chapter Mensuration

(6) Describe how the two figures at the right are alike and how they are different. Which box has larger lateral surface area?

 

Diagram of Question 6 of Exercise 11.3 of NCERT Chapter Mensuration                    

(7) A closed cylindrical tank of radius 7 m and height 3 m is made from a sheet of metal. How much sheet of metal is required?

Ans-

 

Diagram of Question 7 of Exercise 11.3 of NCERT Chapter Mensuration

(8) The lateral surface area of a hollow cylinder is 4224 cm2. It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of rectangular sheet?

Ans-

Diagram of Question 8 of Exercise of 11.3 of NCERT Chapter Mensuration

(10) A company packages its milk powder in cylindrical container whose base has a diameter of 14 cm and height 20 cm. Company places a label around the surface of the container ( as shown in the figure). If label is placed 2 cm from the top and bottom, what is the area of the label.

 

Diagram of Question 10 of Exercise 11.3 of NCERT Chapter Mensuration

Exercise 11.4

(1) Given a cylindrical tank, in which situation will you find surface area and in which situation volume.

(a) To find how much it can hold.

(b) Number of cement bags required to plaster it.

(c) To find the number of smaller tanks that can be filled with water from it.

Ans-

(a) To find how much it can hold.  Volume

(b) Number of cement bags required to plaster it.  Surface area

(c) To find the number of smaller tanks that can be filled with water from it.   Volume

 

(2) Diameter of cylinder A is 7 cm. Without doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders. Check whether the cylinder with greater volume also has greater surface area?

 

Diagram of Question 2 of Exercise 11.4 of NCERT Chapter Mensuration     

Helping Topics

Mensuration

Worksheet Class 8

 

Leave a comment