# Mensuration Part 3: Advance math series 2000 most important questions.

## Mensuration Part 3: Advance math series 2000 most important questions.

Mensuration Part 3: Advance math series 2000 most important questions.

Q641. Each of the measure of the radius of base of a cone and that of a sphere is 8 cm. Also, the volumes of these two solids are equal. The slant height of the cone is

(a) 8√17 cm

(b) 4√17 cm

(c) 34√2 cm

(d) 34 cm.

Q642. If the circumference of a circle is reduced by 50%, its area will be reduced by

(a) 12.5%

(b) 25%

(c) 50%

(d) 75%

Q643. The volume of a sphere is  (88/21)*(14)3 cm3. The curved surface of the sphere is

(a) 2424 cm2

(b) 2446 cm2

(c) 2484cm2

(d) 2464 cm2

Q644. The diameters of two hollow spheres made from the same metal sheet are 21 cm and 17.5 cm respectively. The ratio of the areas of metal sheets required for making the two spheres is

(a) 6 : 5

(b) 36 : 25

(c) 3 : 2

(d) 18 : 25

Q645. A circle is inscribed in a square. An equilateral triangle of side 4√3 cm is inscribed in that circle. The length of the diagonal of the square in centimeters is

(a) 4√2

(b) 8

(c) 8√2

(d) 16

Q646. The length of a rectangular hall is 5m more than its breadth. The area of the hall is 750m2. The length of the hall is:

(a) 15m

(b) 22.5m

(c) 25m

(d) 30m

Q647. The area of the largest triangle, that can be inscribed in a semicircle of radius r cm, is

(a) 2r cm2

(b) r2 cm2

(c) 2r2 cm2

(d) 1/2 r2 cm2

Q648. The diameter of the base of a cylindrical drum is 35 dm., and the height is 24 dm. It is full of kerosene. How many tins each of size 25cm×22cm×35cm can be filled with kerosene from the drum?

(a) 1200

(b) 1020

(c) 600

(d) 120

Q649. A hollow spherical metallic ball has an external diameter 6 cm and is  1/2 cm thick. The volume of the ball (in cm3) is

(a) 41

(b) 37

(c) 47

(d) 40

Q650. If the volumes of two cubes are in the ratio 27: 1,the ratio of their edges is

(a) 3: 1

(b) 27: 1

(c) 16: 1

(d) 4: 1

Q651. If the volumes of two cubes are in the ratio 27: 64, then the ratio of their total surface areas is:

(a) 27: 64

(b) 3: 4

(c) 9: 16

(d) 3: 8

Q652. The area of the incircle of an equilateral triangle of side 42 cm is

(a) 231 cm2

(b) 462 cm2

(c) 22√3 cm2

(d) 924 cm2

Q653. A wooden box measures 20 cm by 12 cm by 10 cm. Thickness of wood is 1 cm. Volume of wood to make the box (in cubic cm) is

(a) 960

(b) 519

(c) 2400

(d) 1120

Q654. A cuboidal block of 6 cm×9cm×12cm is cut up into exact number of equal cubes. The least possible number of cubes will be

(a) 6

(b) 9

(c) 24

(d) 30

Q655. The area of a regular hexagon of side 2√3 cm is:

(a) 18√3 cm2

(b) 12√3 cm2

(c) 36√3 cm2

(d) 27√3 cm2

Q656. If the radius of the base of a cone be doubled and height is left unchanged. Then ratio of the volume of new cone to that of the original cone will be:

(a) 1: 4

(b) 2: 1

(c) 1: 2

(d) 4: 1

Q657. The perimeter of a rhombus is 40 cm. If the length of one of its diagonals be 12 cm, the length of the other diagonal is’

(a) 14 cm

(b) 15 cm

(c) 16 cm

(d) 12 cm

Q658. Spheres A and B have their radii 40 cm and 10 cm respectively. Ratio of surface area of A to the surface area of B is:

(a) 1: 16

(b) 4: 1

(c) 1: 4

(d) 16: 1

Q659. A cistern 6m long and 4 m wide, contains water up to a depth of 1 m 25 cm. The total area of the wet surface is

(a) 55m2

(b) 53.5m2

(c) 50m2

(d) 49m2

Q660. Three coins of the same size (radius 1 cm) are placed on a table such that each of them touches the other two. The area enclosed by the coins is

(a)  cm2                    ‘

(b)  cm2

(c)  cm2

(d)  cm2

Q661. The ratio of bases of two triangles is x: y and that of their areas is a: b. Then the ratio of their corresponding altitudes will be:

(a)

(b) ax : by

(c) ay : bx

(d)

Q662. The ratio of land to water on the whole of the earth is 1: 2, and it is 2: 3 on the northern hemisphere. The ratio of and to water on the southern hemisphere is:

(a) 11: 4

(b) 4: 11

(c) 15: 4

(d) 4: 15

Q663. The percentage increase in the area of a rectangle, if each of its sides is increased by 20%, is:

(a) 40%

(b) 42%

(c) 44%

(d) 46%

Q664. A cube of edge 5 cm is cut into cubes each of edge of 1 cm. The ratio of the total surface area of one of the small cubes to that of the large cube is equal to:

(a) 1: 125

(b) 1: 5

(c) 1: 625

(d) 1: 25

Q665. The perimeter of a rhombus is 40 m and its height is 5m. Its area is:

(a) 60 m2

(b) 50 m2

(c) 45 m2

(d) 55 m2

Q666. If D and E are the mid-points of the sides AB and AC respectively of the ABC in the figure given here, the shaded region of the triangle is what per cent of the whole triangular region?

(a) 50%

(b) 25%

(c) 75%

(d) 60%

Q667. The length of the perpendiculars drawn from any point in the interior of an equilateral triangle to the respective sides are p1, p2 and p3. The length of each side of the triangle is

(a)  2/√3(p1 + p2 + p3)

(b)   1/3(p1 + p2 + p3)

(c)  1/√3(p1 + p2 + p3)

(d)  4/√3(p1 + p2 + p3)

Q668. The length of a rectangle is decreased by 10% and its breadth is increased by 10%. By what per cent is its area changed?

(a) 0%

(b) 1%

(c) 5%

(d) 100%

Q669. A hollow cylindrical tube 20 cm long, is made of iron and its external and internal diameters are 8 cm and 6 cm respectively. The volume of iron used in making the tube is

(a) 1760 cu.cm.

(b) 880 cu. Cm.

(c) 440 cu. cm

(d) 220 cu. Cm.

Q670. The diameter of the iron ball used for the shot-put game is 14cm. It is melted and then a solid cylinder of height 2 *(1/3) cm is made. What will be the diameter of the base of the cylinder?

(a) 14 cm

(b) 28 cm

(c) 14/3cm

(d)  28/3cm

Q671. The area of the greatest circle, which can be inscribed in a square whose perimeter is 120 cm, is:

(a)

(b)

(c)

(d)

Q672. Diameter of a wheel is 3 cm. The wheel revolves 28 times in a minute. To cover 5.280 km distance, the wheel will take

(a) 10 minutes

(b) 20 minutes

(c) 30 minutes

(d) 40 minutes

Q673. If the diagonals of two squares are in the ratio of 2: 5, their areas will be in the ratio of

(a) √2: √5

(b) 2: 5

(c) 4 : 25

(d) 4 : 5

Q674. The ratio of the outer and the inner perimeters of a circular path is 23: 22. If the path is 5 metres wide, the diameter of the inner circle is:

(a) 110m

(b) 55m

(c) 120m

(d) 60m

Q675. If both the radius and height of a right circular cone are increased by 20%, its volume will be increased by

(a) 20%

(b) 40%

(c) 60%

(d) 72.8%

Q676. The length of the longest rod that can be placed in a room which is 12 m long, 9 m broad and 8 m high is

(a) 27 m

(b) 19 m

(c) 17 m

(d) 13 m

Q677. The circum-radius of an equilateral triangle is 8 cm. The in radius of the triangle is

(a) 3.25 cm

(b) 3.50 cm

(c) 4 cm

(d) 4.25 cm

Q678. The difference between the length and breadth of a rectangle is 23m. If its perimeter is 206 m, then its area is

(a) 1520 m2

(b) 2420 m2

(c) 2480 m2

(d) 2520 m2

Q679. The radius of a circular wheel is 1.75 m. The number of revolutions that it will make in travelling 11 km., is

(a) 1000

(b) 10,000

(c) 100

(d) 10

Q680. A circular wire of diameter 42 cm is folded in the shape of a rectangle whose sides are in the ratio 6: 5. Find the area enclosed by the rectangle.

(a) 540 cm2

(b) 1080 cm2

(c) 2160 cm2

(d) 4320 cm2

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