Mensuration (Part-10)

21. A solid hemisphere of radius 8 cm is melted into N identical cone whose radius is 4 cm and height is 2 cm. Then, what is the value of N? [SSC MTS 17/05/2023 (Afternoon)]

(a) 26
(b) 10
(c) 32
(d) 25

Correct Answer: (c) 32

Solution:

22. The ratio of the outer and the inner circumferences of a circular path is 11:7. If path is 20 metres wide, then what is the radius of the inner circle? [SSC MTS 17/05/2023 (Evening)]

(a) 20 metres
(b) 55 metres
(c) 65 metres
(d) 35 metres

Correct Answer: (d) 35 metres

Solution:

23. The longest side of the obtuse triangle is 7 cm and the other two sides of the triangle are 4 cm and 5 cm. Find the area of the triangle. [SSC MTS 18/05/2023 (Morning)]

(a) 1√3 cm²
(b) 6√3 cm²
(c) 3√2 cm²
(d) 4√6 cm²

Correct Answer: (d) 4√6 cm²

Solution:

24. If the diagonal of a square is 18.4 cm, then the area of that square is: (in cm²) [SSC MTS 18/05/2023 (Evening)]

(a) 84.64
(b) 338.56
(c) 324.42
(d) 169.28

Correct Answer: (d) 169.28

Solution:

25. A cone and a cylinder have same height and the radius of the cone is twice of the radius of the cylinder. What is the ratio of the volume of the cone to that of the cylinder? [SSC MTS 19/05/2023 (Afternoon)]

(a) 2:5
(b) 4:5
(c) 3:2
(d) 4:3

Correct Answer: (d) 4:3

Solution:

26. The difference between the length and breadth of a rectangle is 40 metres. If its perimeter is 96 metres, then what will be the area of rectangle? [SSC MTS 19/05/2023 (Evening)]

(a) 254 metre²
(b) 110 metre²
(c) 176 metre²
(d) 152 metre²

Correct Answer: (c) 176 metre²

Solution:

27. A farmer's land is in the shape of a trapezium which has its parallel sides measuring 7.58 yards and 6.42 yards and the distance between the parallel sides is 6.50 yards. The cost of ploughing the land is Rs. 2000 per square yard. What amount have to be spent in order to plough the entire land ? [SSC MTS 13/06/2023 (Morning)]

(a) Rs. 85000
(b) Rs. 91000
(c) Rs. 72000
(d) Rs. 102000

Correct Answer: (b) Rs. 91000

Solution:

28. If the radius of a cylinder is decreased by 12 percent, then by how much percent its height must be increased so that the volume of the cylinder remains same? [SSC MTS 14/06/2023 (Morning)]

(a) 29.13 percent
(b) 21.78 percent
(c) 42.56 percent
(d) 34.27 percent

Correct Answer: (a) 29.13 percent

Solution:

29. The radius of a right circular cylinder is 7 cm. Its height is thrice its radius. What is the curved surface area of the cylinder? [SSC MTS 14/06/2023 (Afternoon)]

(a) 724 cm²
(b) 666 cm²
(c) 924 cm²
(d) 264 cm²

Correct Answer: (c) 924 cm²

Solution:

30. The ratio of the sides of a triangle is 3:3:4. If the area of triangle is 32√5 cm², then what is the length of the equal sides? [SSC MTS 14/06/2023 (Evening)]

(a) 12 cm
(b) 16 cm
(c) 10 cm
(d) 15 cm

Correct Answer: (a) 12 cm

Solution:

Mensuration (Part-10)

21. A solid hemisphere of radius 8 cm is melted into N identical cone whose radius is 4 cm and height is 2 cm. Then, what is the value of N? [SSC MTS 17/05/2023 (Afternoon)]

22. The ratio of the outer and the inner circumferences of a circular path is 11:7. If path is 20 metres wide, then what is the radius of the inner circle? [SSC MTS 17/05/2023 (Evening)]

23. The longest side of the obtuse triangle is 7 cm and the other two sides of the triangle are 4 cm and 5 cm. Find the area of the triangle. [SSC MTS 18/05/2023 (Morning)]

24. If the diagonal of a square is 18.4 cm, then the area of that square is: (in cm²) [SSC MTS 18/05/2023 (Evening)]

25. A cone and a cylinder have same height and the radius of the cone is twice of the radius of the cylinder. What is the ratio of the volume of the cone to that of the cylinder? [SSC MTS 19/05/2023 (Afternoon)]

26. The difference between the length and breadth of a rectangle is 40 metres. If its perimeter is 96 metres, then what will be the area of rectangle? [SSC MTS 19/05/2023 (Evening)]

28. If the radius of a cylinder is decreased by 12 percent, then by how much percent its height must be increased so that the volume of the cylinder remains same? [SSC MTS 14/06/2023 (Morning)]

29. The radius of a right circular cylinder is 7 cm. Its height is thrice its radius. What is the curved surface area of the cylinder? [SSC MTS 14/06/2023 (Afternoon)]

30. The ratio of the sides of a triangle is 3:3:4. If the area of triangle is 32√5 cm², then what is the length of the equal sides? [SSC MTS 14/06/2023 (Evening)]

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