*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?**

**(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 m ^{2}.**

**(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.**

**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.**

**(2)** **The area of a trapezium is 34 cm ^{2} 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-**

**(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.**

**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.**

**(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 m ^{2} and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.**

**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 m^{2}

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.**

**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?**

**Ans-**

**Joyti’s method**

**Kavita’s method**

**(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.**

**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?**

**(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.**

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

**(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-**

**(8)** **The lateral surface area of a hollow cylinder is 4224 cm ^{2}. It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of rectangular sheet?**

**Ans-**

**(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.**

**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?**

**Helping Topics**