Comparing Areas Using Ratios

Q.

A small pizza has diameter of 20 cm and a large pizza has a diameter of 30 cm. George had 50% of the small pizza and Rajdeep had 25% of the large pizza. Who ate more pizza? (Assume that both pizzas have same thickness)

1. the same as that of the medium pizza

2. less than that of the medium pizza

3. more than that of the medium pizza

4. can't be determined

Q.

Area of two squares are in the ratio 4 : 9, find the ratio of their sides.

1. 3 : 2

2. 2 : 3

3. None of these

4. 4 : 9

Q. The areas of two squares are in the ratio 49 : 64. Find the ratio of their sides.

1. 7:8
2. 6:5
3. 5:6
4. 8:7

Q. Three numbers are in the ratio $3:2:5$ and the sum of their squares is $1862$. What are the three numbers?

1. $18,12,30$
2. $24,16,40$
3. $21,14,35$
4. $15,10,25$

Q.

Two rectangles have the same perimeter. Length and breadth are in the ratio 2 : 3 in The 1st and 3 : 4 in the 2nd.

The 1st one has greater Area.

1. True

2. False

Q.

The triangle ABC is given below :

The areas of AOB and AOC are in the ratio 14 : 20

If the area of the smaller triangle is $24c{m}^2$ less than the area of larger triangle, find the total area of the triangle ABC.

1. $162c{m}^2$

2. $156c{m}^2$

3. $136c{m}^2$

4. $142c{m}^2$

Q. The sum of the squares of three numbers which are in the ratio $2:3:4$ is $725.$ What are these numbers?

1. $10,15,20$
2. $14,21,28$
3. $20,30,40$
4. $20,15,30$

Q.

The area of two triangles are in the ratio 8 : 12. If the ratio between bases is also the same and the area of smaller triangle is 20 less than area of bigger triangle,

Find the area of the bigger triangle in square cm.

1. $50c{m}^2$

2. $72c{m}^2$

3. $60c{m}^2$

4. $48c{m}^2$

Q.

The ratio of areas of a circular and rectangular field is 1:2. If the area of a circular field is 50 m², then area of the rectangular field is ___ m²

Q. Amar drew a square. He then erased it and drew a second square whose sides were $3$ times the sides of the first square. By what percent was the area of the square increased?

1. $200\%$
2. $800\%$
3. $400\%$
4. $600\%$

Q.

The ratio of areas of a circular and rectangular field is 1:2. Find the area of the rectangular field if the area of a circular field is 50 m².

1. None of these

2. 25 m²

3. 50 m²

4. 100 m²

Q.

A path of uniform width 1.5 m runs around the outside of a rectangular field 18 m by 15 m. The area of the path is _____ $m^2$.

1. 108

2. 100

3. 96

4. 90

Q.

Question 9 (i)

The adjoining figure represents a rectangular lawn with a circular flower bed in the middle. Find:

The area of the whole land.

Q.

Question 9 (iii)

The adjoining figure represents a rectangular lawn with a circular flower bed in the middle. Find:

The area of a lawn excluding the area of the flower bed.