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Mensuration

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Q 1. The area of a rectangular field is {tex} 144 \mathrm { m } ^ { 2 } {/tex}. If the length had been 6 metres more, the area would have been {tex} 54 \mathrm { m } ^ { 2 } {/tex} more. The original length of the field is

22 metres

18 metres

16 metres

24 metres

None of these

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Q 2. The altitude drawn to the base of an isosceles triangle is 8 {tex} \mathrm { cm } {/tex} and the perimeter is {tex} 32\ \mathrm { cm } . {/tex} The area of the triangle is

{tex} 72 \ \mathrm { cm } ^ { 2 } {/tex}

{tex} 60 \ \mathrm { cm } ^ { 2 } {/tex}

{tex} 66 \ \mathrm { cm } ^ { 2 } {/tex}

{tex} 65\ \mathrm { cm } ^ { 2 } {/tex}

None of these

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Q 3. Four equal circles are described about the four corners of a square so that each touches two of the others. If a side of the square is {tex} 14 \mathrm { cm } , {/tex} then the area enclosed between the circumferences of the circles is:

{tex} 24 \mathrm { cm } ^ { 2 } {/tex}

{tex} 42 \mathrm { cm } ^ { 2 } {/tex}

{tex} 154 \mathrm { cm } ^ { 2 } {/tex}

{tex} 196 \mathrm { cm } ^ { 2 } {/tex}

None of these

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Q 4. The area of a side of a box is {tex} 120 \mathrm { sq } \mathrm { cm } . {/tex} The area of the other side of the box is {tex} 72 \mathrm { sq } \mathrm { cm } . {/tex} If the area of the upper surface of the box is {tex} 60 \mathrm { sq } \mathrm { cm } {/tex} then find the volume of the box.

{tex} 259200 \mathrm { cm } ^ { 3 } {/tex}

{tex} 86400 \mathrm { cm } ^ { 3 } {/tex}

{tex} 720 \mathrm { cm } ^ { 3 } {/tex}

Cannot be determined

None of these

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Q 5. The capacity of a cylindrical tank is 246.4 litres. If the height is 4 metres, what is the diameter of the base?

1.4 metres

2.8 metres

28 metres

14 metres

None of these

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Q 6. A square carpet with an area {tex} 169 \mathrm { m } ^ { 2 } {/tex} must have 2 metres cut-off one of its edges in order to be a perfect fit for a rectangular room. What is the area of rectangular room?

{tex} 180 \mathrm{m ^ { 2 }} {/tex}

{tex} 164 \mathrm{m ^ { 2 }} {/tex}

{tex} 152 \mathrm { m } ^ { 2 } {/tex}

{tex} 143 \mathrm{m ^ { 2 }} {/tex}

None of these

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Q 7. The area of a right-angled triangle is two-thirds of the area of a rectangle. The base of the triangle is 80 percent of the breadth of the rectangle. If the perimeter of the rectangle is {tex} 200 \mathrm { cm } , {/tex} what is the height of the triangle?

{tex} 20 \mathrm { cm } {/tex}

{tex} 30 \mathrm { cm } {/tex}

{tex} 15 \mathrm { cm } {/tex}

Data inadequate

None of these

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Q 8. A circular ground whose diameter is 35 metres, has a 1.4 metre-broad garden around it. What is the area of the garden in square metres?

160.16

6.16

122.66

Data inadeuate

None of these

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Q 9. A rectangular garden has a 5 -metre-wide road outside around all the four sides. The area of the road is 600 square metres. What is the ratio between the length and the breadth of that plot?

3:2

4:3

5:4

Data inadequate

None of these

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Q 10. A cube of 384{tex} \mathrm { cm } ^ { 2 } {/tex} surface area is melted to make x number of small cubes each of 96{tex} \mathrm { mm } ^ { 2 } {/tex} surface area. The value of {tex} \mathrm { x } {/tex} is

80,000

8

8,000

800

None of these

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Q 11. If the perimeter and diagonal of a rectangle are 14{tex} \mathrm { cm } {/tex} and 5 {tex} \mathrm { cm } {/tex} respectively, find its area.

12{tex} \mathrm { cm } ^ { 2 } {/tex}

16{tex} \mathrm { cm } ^ { 2 } {/tex}

20{tex} \mathrm { cm } ^ { 2 } {/tex}

24{tex} \mathrm { cm } ^ { 2 } {/tex}

None of these

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Q 12. The length, breadth and height of a cuboid are in the ratio {tex} 1 : 2 : 3 . {/tex} The length, breadth and height of the cuboid are increased by {tex} 100 \% , 200 \% {/tex} and {tex} 200\% {/tex} , respectively. Then, the increase in the volume of the cuboid will be:

5 times

6 times

12 times

17 times

None of these

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Q 13. The ratio of the length to the breadth of a rectangular plot is {tex} 6 : 5 {/tex} respectively; if the breadth of the plot is 34 metre less than the length, what is the perimeter of the rectangular plot?

374 metres

408 metre

814 metre

748 metre

None of these

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Q 14. A rectangular plot {tex} 15 \mathrm { m } \times 10 \mathrm { m } {/tex} has a path of grass outside it. If the area of grassy pathway is {tex} 54 \mathrm { m } ^ { 2 } , {/tex} find the width of the path.

4{tex} \mathrm { m } {/tex}

3{tex} \mathrm { m } {/tex}

2{tex} \mathrm { m} {/tex}

{tex}1 \mathrm { m } {/tex}

None of these

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Q 15. The length of a rectangular plot is twice its breadth. If the area of the rectangular plot is 2592 sq metres, what is the length of the rectangular plot?

76 metre

36 metre

74 metre

37 metre

None of these

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Q 16. Four sheets of {tex} 50 \mathrm { cm } \times 5 \mathrm { cm } {/tex} are arranged without overlapping to form a square having side {tex} 55 \mathrm { cm } . {/tex} What is the area of the inner square so formed?

2500{tex} \mathrm { cm } ^ { 2 } {/tex}

2025{tex} \mathrm { cm } ^ { 2 } {/tex}

{tex}1600 \mathrm { cm } ^ { 2 } {/tex}

1650{tex} \mathrm { cm } ^ { 2 } {/tex}

None of these

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Q 17. If the area of a circle decreases by {tex} 36 \% , {/tex} then the radius of the circle decreases by

20{tex} \% {/tex}

18{tex} \% {/tex}

36{tex} \% {/tex}

64{tex} \% {/tex}

None of these

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Q 18. Area of a rectangle is equal to the area of the circle whose radius is {tex}21 \mathrm { cm } {/tex} . If the length and the breadth of the rectangle are in the ratio of {tex} 14 : 11 {/tex} respectively, what is its perimeter?

{tex}142 \mathrm { cm } {/tex}

{tex}140 \mathrm { cm } {/tex}

{tex}132 \mathrm{\, cm } {/tex}

{tex}150 \mathrm { \,cm } {/tex}

None of these

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Q 19. The length of a rectangular field is double its width. Inside the field there is a square-shaped pond 8{tex} \mathrm { m } {/tex} long. If the area of the pond is 1/8 of the area of the field, what is the length of the field?

32{tex} \mathrm { m } {/tex}

16{tex} \mathrm { m } {/tex}

64{tex} \mathrm { m } {/tex}

20{tex}\mathrm {\, m }{/tex}

None of these

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Q 20. 20 buckets of water fill a tank when the capacity of each bucket is 13.5 litres. How many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres?

30

32

60

Data inadequate

None of these

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Q 21. A right circular cone is exactly fitted inside a cube in such a way that the edges of the base of the cone are touching the edges of one of the faces of the cube and the vertex is on the opposite face of the cube. If the volume of the cube is {tex} 343 \mathrm { cc } , {/tex} what approximately is the volume of the cone ?

{tex} 80 \mathrm { cc } {/tex}

{tex} 90 \mathrm { cc } {/tex}

{tex} 110 \mathrm { cc } {/tex}

{tex} 105 \mathrm { cc } {/tex}

{tex} 100 \mathrm { cc } {/tex}

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Q 22. The intermal measurements of a box with lid are {tex} 115 \times 75 \times 35 {/tex} {tex} \mathrm { cm } ^ { 3 } {/tex} and the wood of which it is made is {tex} 2.5 \ \mathrm { cm } {/tex} thick. Find the volume of wood.

{tex} 82,125 \mathrm { cm } ^ { 3 } {/tex}

{tex} 70,054 \mathrm { cm } ^ { 3 } {/tex}

{tex} 78,514 \mathrm { cm } ^ { 3 } {/tex}

Data inadequate

None of these

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Q 23. The ratio between the length and the breadth of a rectangular plot is {tex} 7: 5 . {/tex} If the perimeter of the plot is 144 metres, what is its area?

1320 sq. metres

1260 sq. metres

1280 sq. metres

1380 sq. metres

None of these

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Q 24. A rectangular paper, when folded into two congruent parts had a perimeter of {tex} 34 \mathrm { cm } {/tex} for each part folded along one set of sides and the same is {tex} 38 \mathrm { cm } {/tex} when folded along the other set of sides. What is the area of the paper?

{tex} 140 \mathrm { cm } ^ { 2 } {/tex}

{tex} 240 \mathrm { cm } ^ { 2 } {/tex}

{tex} 560 \mathrm { cm } ^ { 2 } {/tex}

{tex} 160 \mathrm { cm } ^ { 2 } {/tex}

None of these

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Q 25. A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and the height are in the ratio {tex} 5 : 12 , {/tex} then the ratio of the total surface area of the cylinder to that of the cone is

{tex} 3 : 1 {/tex}

{tex} 13 : 9 {/tex}

{tex} 17 : 9 {/tex}

{tex} 34 : 9 {/tex}

None of these

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