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## PATWARI MENSURATION || TEST 2020 || PATWARI TEST-2020

#### Mensuration

Q1. Find the total surface area of a pyramid having a slant height of 8 cm and a base which is a square of side 4 cm (in cm square)?
(a) 80
(b) 64
(c) 72
(d) 84

Q2. A prism and a pyramid have the same base and the same height. Find the ratio of the volumes of the prism and the pyramid.
(a) 1 : 1
(b) 1 : 3
(c) 3 : 1
(d) Cannot be determined

Q3. A solid metallic cylinder of base radius 3 cm and height 5 cm is melted to form cones, each of height 1 cm and base radius 1 mm. The number of cones is
(a) 7500
(b) 13500
(c) 3500
(d) 4500

Q4. The base of a right prism is a trapezium whose lengths of two parallel sides are 10 cm and 6 cm and distance between them is 5 cm. If the height of the prism is 8 cm, its volume is:
(a) 300 cm cube
(b) 300.5 cm cube
(c) 320 cm cube
(d) 310 cmcube

Q5. The base of a solid right prism is a triangle whose sides are 9 cm, 12 cm, and 15 cm. The height of the prism is 5 cm. Then, the total surface area of the prism is
(a) 180 cm square
(b) 234cm square
(c) 288 cm square
(d) 270 cm square

Q6. Area of the base of a pyramid is 57 sq. cm. and height is 10 cm, then its volume in cm cube, is
(a) 570
(b) 390
(c) 190
(d) 590

Q7. The base of a right prism is a trapezium. The lengths of the parallel sides are 8 cm and 14 cm and the distance between the parallel sides is 8 cm. If the volume of the prism is 1056 cm cube, then the height of the prism is
(a) 44 cm
(b) 16.5 cm
(c) 12 cm
(d) 10.56 cm

Q8. The base of a right pyramid is a square of side 16 cm long. If its height be 15 cm, then the area of the lateral surface in square centimeter is:
(a) 136
(b) 544
(c) 800
(d) 1280

Q9. The height of a right prism with a square base is 15 cm. If the area of the total surface of the prism is 608 sq. cm, its volume is
(a)  910 cm cube
(b) 920 cm cube
(c)  960 cm cube
(d) 980 cm cube

Q10. If the radius of a cylinder is increased by 25% and its height remains unchanged, then find the per cent increase in volume.
(a) 56.25%
(b) 52.25%
(c) 50.4%
(d) 60.25%

Q11. If the radius of cylinder is decreased by 8%, while its height is increased by 4%, what will be the effect on volume?
(a) 11.9744% (decrease)
(b) 11.9744% (increase)
(c) 12.4678% (decrease)
(d) 12.4678% (increase)

Q12. A rod of 2 cm diameter and 30 cm length is converted into an electric wire of 3 m length of uniform thickness. The diameter of the wire is
(a)  2/10 cm
(b) 2/√10 cm
(c) 1/√10 cm
(d) 1/10 cm

Q13. What is the height of a solid cylinder of radius 5 cm and total surface area is 660 sq cm?
(a) 10 cm
(b) 12 cm
(c) 15 cm
(d) 16 cm

Q14. The frustum of a right circular cone has the diameters of base 10 cm, of top 6 cm and a height of 5 cm. Find its slant height.
(a) √29 cm
(b) 3√3 cm
(c) √13 cm
(d) 4√3 cm

Q15. A cone of radius r cm and height h cm is divided into two parts by drawing a plane through the middle point of its height and parallel to the base. What is the ratio of the volume of the original cone to the volume of the smaller cone?
(a) 4 : 1
(b) 8 : 1
(c) 2 : 1
(d) 6 : 1

Solutions

S1. Ans.(a)
Sol.

S2. Ans.(c)
Sol.

S3. Ans.(b)
Sol.

S4. Ans.(c)
Sol.

S5. Ans.(c)
Sol.

S6. Ans. (c)
Sol.

S7. Ans. (c)
Sol.

S8. Ans. (b)
Sol.

S9. Ans. (c)
Sol.

S10. Ans.(a)
Sol.

S11. Ans.(a)
Sol.

S12. Ans.(b)
Sol.

S13. Ans.(d)
Sol.

S14. Ans.(a)
Sol.

S15. Ans.(b)
Sol.