Q.11 A gold bar in the shape of a rectangular solid, 36 cm long, 9 cm broad and 6 cm high, is to be melted and cast into two different cubes, the volume the bigger being eight times that of the smaller. The surface is of the smaller cube, in cm² is….
(A) 36
(B) 216
(C) 72
(D) 144
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Q.12 If base diameter and the height of a right circular cone are each increased by 100%, then the volume of the will increase by….
(A) 100%
(B) 200%
(C) 400%
(D) 700%
Q.13 If a solid metal cylinder of radius 4 cm and height 10 cm, is melted to make solid balls of radius 1 mm, then number of such balls produced (in lakhs) will be.
(A) 0.8 lakh
(B) 1.0 lakh
(C) 1.2 lakh
(D) 1.4 lakh
Q.14 If a rectangular paper of length 30 cm and width 12 cm is rolled to from a cylinder with height equal to width of the paper, then its base radius will be…
(A) 18/π
(B) 15/ π cm
(C) 15/2 π cm
(D) 9/2 π cm
Q.15 If diameter of the base of right circular cylinder is r and its height is equal to radius of base, then its volume is….
(A) 1/8 πr²
(B) πr³
(C) 2πr³
(D) 4πr³
Q.16 If numerical value of the curved surface area of a right circular cylinder is equal to numerical value of its volume, then numerical value of the radius of the base of the cylinder is….
(A) 4
(B) 3
(C) 2
(D) 1
Q.17 If edges of a cuboid are 3 cm, 4 cm and 12 cm, then length of its diagonal will be.
(A) Ö5 cm
(B) Ö19 cm
(C) 12 cm
(D) 13 cm
Q.18 The area of a rhombus with side 50 dm and one of the diagonals 80 dm, is…
(A) 1600 dm²
(B) 500 dm²
(C) 1200 dm²
(D) 2500 dm²
Q.19 If side of a square is 4 m, then area of the square in m² drawn on its diagonal is….
(A) 16
(B) 32
(C) 16Ö2
(D) 32Ö2
Q.20Volume of a right circular cylinder and the volume of a sphere (whose radius is same as that of cylinder) are equal. If the height of the cylinder is….
(A) 4/5 times of its radius
(B) 4/3 times if its radius
(C) equal to its radius
(D) equal to its diameter
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Q.21 If a spherical lead of radius 20 cm is melted and small lead balls of radius 2 cm are made, then the total number of possible small lead balls is….
(A) 8000
(B) 800
(C) 80
(D) 100
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Q.22 The number of rounds that a wheel of diameter 7 m will make in going 4.4 km is….
(A) 1000
(B) 800
(C) 2000
(D) 100
Q.23 A plot of land is the shape of a right angled isosceles triangle. Length of the hypotenuse side is 50Ö2 and cost of the fencing is Rs. 3 per meter. The cost of fencing the plot will be.
(A) Rs. 381
(B) Rs. 341
(C) Rs. 391
(D) Rs. 371
Q.24 A 10 m wide lawn is cultivated all along the outside of a rectangular plot measuring 100 m x 50 m. The total area of the lawn is….
(A) 750 m²
(B) 5000 m²
(C) 2800 m²
(D) 2400 m²
Q.25 A circle and square have same area. Therefore, ratio of the side of the square and radius of the circle is….
(A) Öπ: 1
(B) 1: Öπ
(C) 1: π
(D) π: 1
Q.26 A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The difference between the surface areas of the two solids will be…
(A) 386 cm²
(B) 286 cm²
(C) 276 cm²
(D) 376 cm²
Q.27 If a right cylinder and a right circular cone have the same radius and same volume, then ratio of height of the cylinder to that of the cone is….
(A) 3: 2
(B) 2: 3
(C) 3: 1
(D) 1: 3
Q.28 A reservoir is in the shape of a frustum of a right circular cone. It is 8 cm across at the top and 4 cm across at the bottom. It is 6 cm deep. Its capacity is.
(A) 176 m³
(B) 186 m³
(C) 88 m³
(D) 93 m³
Q.29 The dimensions of the floor of a rectangular hall are 60 m x 50 m. The floor of this hall is to be titled fully with 20 cm x 10 cm rectangular tiles without breaking them to smaller size. The number of tiles required is…
(A) 100000
(B) 160000
(C) 150000
(D) 50000
Q.30 Length of the longest rod that can be placed in a room 30 m long, 25 m broad and 18 m high is….
(A) 30 m
(B) 15 Ö2
(C) 60 m
(D) 30 Ö2 m
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