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Mensuration Part 4: Advance math series 2000 most important questions.

Mensuration Part 4: Advance math series 2000 most important questions.

Q681. A sphere of radius 2 cm is put into water contained in a cylinder of base-radius 4 cm. if the sphere is completely immersed in the water, the water level in the cylinder rises by

(a) 1/3 cm

(b) 1/2 cm

(c) 2/3 cm

(d) 2 cm

Q682. The perimeter of a rhombus is 40 cm. If one of the diagonals be 12 cm long, what is the length of the other diagonal?

(a) 12 cm

(b) √136

(c) 16 cm

(d) √44 cm

Q683. Each of the height and base-radius of a cone is increased by 100%.Thepercentae increase in the volume of the cone is

(a) 700%

(b) 400%

(c) 300%

(d) 100%

Q684. Four equal circles each of radius ‘a’ units touch one another. The area enclosed between then  in square units, is

(a) 3a2

(b) 6a2/7

(c) 41a2/7

(d) a2/7

Q685. If the radius of a cylinder is decreased by 50% and the height is increased by 50% to form a new cylinder, the volume will be decreased by

(a) 0%

(b) 25%

(c) 62.5%

(d) 75%

Q686. The diagonals of a rhombus are 32 cm and 24 cm respectively. The perimeter of the rhombus is:

(a) 80 cm

(b) 72 cm

(c) 68 cm

(d) 64 cm

Q687. A took 15 sec, to cross a rectangular field diagonally walking at the rate of 52m/min. and B took the same time to cross the same field along its sides walking at the rate of 68 m/min. The area of the field is:

(a) 30 m2

(b) 40 m2

(c) 50 m2

(d) 60 m2

Q688. The perimeter of two squares are 24 cm and 32 cm. The perimeter (in cm) of a third square equal in area to the sum of the areas of these squares is:

(a) 45

(b) 40

(c) 32

(d) 48

Q689. The side of a triangle are 3 cm, 4 cm and 5 cm. The area (in cm2) of the triangle formed by joining the mid points of this triangle is:

(a) 6

(b) 3

(c)  3/2

(d) 3/4

Q690. If the height of a given cone be doubled and radius of the base remains the same, the ratio of the volume of the given cone to that of the given cone to that of the second cone will be

(a) 2: 1

(b) 1: 8

(c) 1: 2

(d) 8: 1

Q691. Three circles of radius 3.5 cm each are placed in such a way that each touches the other two. The area of the portion enclosed by the circles is

(a) 1.975 cm2

(b) 1.967 cm2

(c) 19.67 cm2

(d) 21.21 cm2

Q692. Four equal sized maximum circular plates are cut off from a square paper sheet of area 784 sq. cm. The circumference of each plate is

(a) 22 cm

(b) 44 cm

(c) 66 cm

(d) 68 cm

Q693. The diagonals of a rhombus are 24 cm and 10 cm. The perimeter of the rhombus (in cm) is:

(a) 68

(b) 65

(c) 54

(d) 52

Q694. The difference of the areas of two squares drawn on two line segments of different lengths is 32 sq. cm. Find the length of the greater line segment if one is longer than the other by 2 cm.

(a) 7 cm

(b) 9 cm

(c) 11 cm

(d) 16 cm

Q695. A can go round a circular path 8 times in 40 minutes. If the diameter of the circle is increased to 10 times the original diameter, the time required by A to go round the new path once travelling at the same speed as before is:

(a) 25 min

(b) 20 min

(c) 50 min

(d) 100 min

Q696. From a point in the interior of an equilateral triangle the perpendicular distances of the sides are  √3 cm, 2√3 cm and 5√3 cm. The perimeter (in cm) of the triangle is

(a) 64

(b) 32

(c) 48

(d) 24

Q697. The height of a conical tank is 60 cm and the diameter of its base is 64 cm. The cost of painting it from outside at the rate of Rs. 35 per sq. m. is:

(a) Rs. 52.00 approx

(b) Rs. 39.20 approx

(c)  Rs. 35.20 approx.

(d) Rs. 23.94 approx.

Q698. The area (in m2) of the square which has the same perimeter as a rectangle whose length is 48 m and is 3 times its breadth is:

(a) 1000

(b) 1024

(c) 1600

(d) 1042

Q699. Three solid spheres of a metal whose radii are 1 cm, 6 cm and 8 cm are melted to form an other solid sphere. The radius of this new sphere is

(a) 10.5 cm

(b) 9.5 cm

(c) 10 cm

(d) 9 cm

Q700. A solid metallic spherical ball of diameter 6 cm is melted and recasted into a cone with diameter of the base as 12 cm. The height of the cone is

(a) 6 cm

(b) 2 cm

(c) 4 cm

(d) 3 cm

Q701. The length, breadth and height of a room is 5 m, 4 m, and 3 m respectively. Find the length of the largest  bamboo that can be kept inside the room.

(a) 5 m

(b) 60 m

(c) 7 m

(d) 5 √2 m

Q702. A cooper rod of 1cm diameter and 8 cm long is formed into a wire of uniform diameter, whose length is 18 m. The radius (in cm) of the wire is

(a) 1/15

(b) 1/30

(c) 2/15

(d) 15

Q703. The area of the greatest circle inscribed inside a square of side 21 cm is

(a) 344.5 cm2

(b) 364.5 cm2

(c) 346.5 cm2

(d) 366.5 cm2

Q704. If the radius of a sphere is increased by 2 cm, its surface area increases by 252 cm2. The radius of the sphere before increase was

(a) 3 cm

(b) 4 cm

(c) 5 cm

(d) 6 cm

Q705. If the area of a triangle with base 12 cm is equal to the area of a square with side 12 cm, the altitude of the triangle will be

(a) 12 cm

(b) 24 cm

(c) 18 cm

(d) 36 cm

Q706. A path of uniform width surrounds a circular park. The difference of internal and external circumferences of this circular path is 132 metres. Its width is:

(a) 22 m

(b) 20 m

(c) 21 m

(d) 24 m

Q707. Three solid metallic spheres of diameters 6 cm, 8 cm and 10 cm are melted and recast into a new solid sphere. The diameter of the new sphere is:

(a) 4 cm

(b) 6 cm

(c) 8 cm

(d) 12 cm

Q708. The ratio of the volume of two cones is 2: 3 and the ratio of radii of their bases is 1: 2. The ratio of their heights is

(a) 3: 8

(b) 8: 3

(c) 4: 3

(d) 3: 4

Q709. Between a square of perimeter 44 cm and a circle of circumference 44 cm, which figure has larger area and by how much?

(a) Square, 33cm2

(b) Circle, 33 cm2

(c) Both have equal area

(d) Square, 495 cm2

Q710. The base of a conical lent is 19.2 metres in diameter and the height of its vertex is 2.8 metres. The area of the canvas required to put up such a tent (in square metres)

(a) 3017.1

(b) 3170

(c) 301.7

(d) 30.17

Q711. The volume of a right circular cylinder is equal to the volume of that right circular cone whose height is 108 cm and diameter of base is 30 cm. If the height of the cylinder is 9 cm, the diameter of its base is

(a) 30 cm

(b) 60 cm

(c) 50 cm

(d) 40 cm

Q712. The base of a triangle is 15 cm and height is 12 cm. The height of another triangle of double the area having the base 20 cm is:

(a) 9 cm

(b) 18 cm

(c) 8 cm

(d) 12.5 cm

Q713. A conical vessel whose internal radius is 12cm and height 50 cm is full of liquid. The contents are emptied into a cylindrical vessel with radius (internal) 10 cm. The height to which the liquid rises in the cylindrical vessel is:

(a) 25 cm

(b) 20 cm

(c) 24 cm

(d) 22 cm

Q714. A cylindrical tank of diameter 35 cm is full of water. If 11 litres of water is drawn off, the water level in the tank will drop by:

(a) 10(1/2) cm

(b) 12 (6/7) cm

(c) 14 cm

(d) 11(3/7) cm

Q715. The volume of a right circular cylinder whose height is 40 cm, and circumference of its base is 66 cm, is:

(a) 55440 cm3

(b) 3465 cm3

(c) 7720 cm3

(d) 13860 cm3

Q716. Three solid metallic balls of radii 3 cm, 4 cm and 5 cm are melted and moulded into a single solid ball. The radius of the new ball is:

(a) 2 cm

(b) 3 cm

(c) 4 cm

(d) 6 cm

Q717. The diagonal of a square A is (a + b). The diagonal of a square whose area is twice the area of square A, is

(a) 2(a + b)

(b) 2(a + b)2

(c) √2(a + b)

(d) √2(a – b)

Q718. A cone of height 7 cm and base radius 1 cm is carved from a cuboidal block of wood 10 cm  Assuming  the percentage wood wasted in the process is:

(a) 92 (2/3) %

(b) 46(1/3)%

(c) 53(2/3) %

(d) 7(1/3)%

Q719. The diagonal of a square is 4√2 cm. The diagonal of another square whose area is double that of the first square is:

(a) 8√2  cm

(b) 16 cm

(c)  √32 cm

(d) 8 cm

Q720. The volume of a cuboid is twice the volume of a cube. If the dimensions of the cuboid are 9 cm, 8 cm and 6 cm, the total surface area of the cube is:

(a) 72 cm2

(b) 216 cm2

(c) 432 cm2

(d) 108 cm2

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