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Mensuration Part 12: Advance Math Series 2000 Most Important Questions.

Mensuration Part 12: Advance Math Series 2000 Most Important Questions. Q962. Area of the in circle of an equilateral triangle with side 6 cm is

(a) π/2 sq.cm.

(b) √3π  sq.cm

(c) 6π  sq.cm.

(d) 3 π sq.cm.

Q963. A cone, a hemisphere and a cylinder stand on equal base and have the same height. Their volumes are in the ratio

(a) 1 : 3 : 2

(b) 2 : 3 : 1

(c) 1 : 2 : 3

(d) 3 : 1 : 2

Q964. If the radii of the circular ends of a truncated conical bucket whichis 45 cm high be 28 cm and 7 cm, then the capacity of the bucket in cubic centimeter is (use π = 22/7)

(a) 48510

(b) 45810

(c) 48150

(d) 48051

Q965. Area of the base of a pyramid is 57 sq.cm. and height is 10 cm, then its volume in cm3, is

(a) 570

(b) 390

(c) 190

(d) 590

Q966. The diameter of a wheel is 98 cm. The number of revolutions in which it will have to cover a distance of 1540 m is

(a) 500

(b) 600

(c) 700

(d) 800

Q967. The rain water from a roof 22 m × 20 m drains into a cylindrical vessel having a diameter of 2 m and height 3.5 m. If the vessel is just full, then the rainfall in cm is:

(a) 2

(b) 2.5

(c) 3

(d) 4.5

Q968. If the perimeter of a square and a rectangle are the same. Then the areas p and Q enclosed by them would satisfy the condition

(a) P < Q

(b) P=< Q

(c) P > Q

(d) P = Q

Q969. Two adjacent sides of a parallelogram are of lengths 15 cm and 18 cm. If the distance between two smaller sides is 12 cm, then the distance between two bigger sides is

(a) 8 cm

(b) 10 cm

(c) 12 cm

(d) 15 cm

Q970. If the perimeter of a semicircular field is 144m, then lthe diameter of the field is(Taken π = 22/7)

(a) 55m

(b) 30m

(c) 28m

(d) 56m

Q971. A parallelogram has sides 15 cm and 7 cm long. The length of one of the diagonals is 20 cm. The area of the parallelogram, is

(a) 42 cm2

(b) 60 cm2

(c) 84 cm2

(d) 96 cm2

Q972. The ratio of the volume of a cube and of a solid sphere is 363 : 49. The ratio of an edge of the cube and the radius of the sphere is(Taken π = 22/7)

(a) 7 : 11

(b) 22 : 7

(c) 11 : 7

(d) 7 : 22

Q973. The ratio of radii of two cones is 3 : 4 and the ratio of their heights is 4 : 3. Then the ratio of their volumes will be

(a) 3 : 4

(b) 4 : 3

(c) 9 : 16

(d) 16 : 9

Q974. The ratio of the areas of a regular hexagon and an equilateral triangle having same perimeter is

(a) 2 : 3

(b) 6 : 1

(c) 3 : 2

(d) 1 : 6

Q975. A copper wire is bent in the shape of a square of area 81cm2. If the same wire is bent in the form of a semicircle, the radius (in cm) of the semicircle is(Taken π = 22/7)

(a) 16

(b) 14

(c) 10

(d) 7

Q976. The lengths of two sides of an isosceles triangle are 15 and 22 respectively. What are the possible values of perimeter?

(a) 52 or 59

(b) 52 or 60

(c) 15 or 37

(d) 37 or 29

Q977. If a right circular cone is separated into solids of volumes V1, V2, V3 by two planes parallel to the base, which also trisect the altitude, then V1 : V2 : V3 is

(a) 1 : 2 : 3

(b) 1 : 4 : 6

(c) 1 : 6 : 9

(d) 1 : 7 : 19

Q978. The length of longest pole that can be placed in a 12m long, 8 m broad and 9 m high room, is

(a) 12 m

(b) 17 m

(c) 19 m

(d) 21m

Q979. The base of a right prism is an equilateral triangle of area 173 cm2 and the volume of the prism is 10380 cm3. The area of the lateral surface of the prism is (use = 1.73)

(a) 1200 cm2

(b) 2400 cm2

(c) 3600 cm2

(d) 4380 cm2

Q980. A cylindrical rod of iron whose height is eight times its radius is melted and cast into spherical balls each of half the radius of the cylinder. The number of such spherical balls is

(a) 12

(b) 16

(c) 24

(d) 48

Q981. The ratio of the areas of the circumcircle and the incircle of an equilateral triangle is

(a) 2 : 1

(b) 4 : 1

(c) 8 : 1

(d) 3 : 2

Q982. The four equal circles of radius 4 cm drawn on the four corners of a square touch each other externally. Then the area of the portion between the square and the four sectors is

(a) 9(π – 4) sq.cm.

(b) 16( π- 4) sq.cm

(c) 9(4 –π ) sq.cm.

(d) 16(4 –π ) sq.cm.

Q983. Two solid right cones of equal heights and of radii r1 and r2 are melted and made to form a solid sphere of radius R. Then the height of the cone is

(a) 4R2/r12 + r22

(b) 4R/r1+r2

(c) 4R3/r12 + r22

(d) R2/r12 + r22

Q984. There is a pyramid on a base which is a regular hexagon of side 2 a cm. If every slant edge of this pyramid is of length 5a/2 cm, then the volume of this pyramid is

(a) 3a3 cm3

(b) 3√2 a3 cm3

(c) 3√3 a3 cm3

(d) 6a3 cm3

Q985. The length of a diagonal of a square is 15cm. Its area is

(a) 112.5 cm2

(b) 450 cm2

(c) 225√2/2  cm2

(d) 225 cm2

Q986. The respective heights and volumes of a hemisphere and a right circular cylinder are equal, then the ratio of their radii is

(a) √2 :√3

(b) √3 : 1

(c) √3 :√2

(d) 2 :√3

Q987. A toy is in the form of a cone mounted on a hemisphere. The radius of the hemisphere and that of the cone is 3 cm and height of the cone is 4 cm. The total surface area of the toy is (Taken π =22/7)

(a) 75.43 sq. cm

(b) 103.71 sq.cm.

(c) 85.35 sq.cm.

(d) 120.71 sq.cm.

Q988. At each corner of a triangular field of sides 26m, 28m and 30m, a cow is tethered by a rope of length 7m. The area (in m2) ungrazed by the cows is

(a) 366

(b) 259

(c) 154

(d) 77

Q989. The volumes of two spheres are in the ratio 8 : 27. The ratio of their surface areas is:

(a) 4 : 9

(b) 2 : 3

(c) 4 : 5

(d) 5 : 6

Q990.The height of the cone is 30 cm. A small cone is cut off at the top by a plane parallel to its base. If its volume is of the volume of the cone, at what height, above the base, is the section made?

(a) 6 cm

(b) 8 cm

(c) 10 cm

(d) 20 cm

Q991. A sphere and a cylinder have equal volume and equal radius. The ratio of the curved surface area of the cylinder to that of the sphere is

(a) 4 : 3

(b) 2 : 3

(c) 3 : 2

(d) 3 : 4

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Q992. The diameter of the base of a right circular cone is 4 cm and its height 2√3cm. The slant height of the cone is

(a) 5 cm

(b) 4 cm

(c) 2√3

(d) 3 cm

Q993. The ratio of the length of the parallel sides of a trapezium is 3 : 2. The shortest distance between them is 15 cm. if the area of the trapezium is 450 cm2, the sum of the lengths of the parallel sides is

(a) 15 cm

(b) 36 cm

(c) 42 cm

(d) 60 cm

Q994. An equilateral triangle and a regular hexagon have the same perimeter. The ratio of the area of the triangle to that of the hexagon is

(a) 3 : 2

(b) 2 : 3

(c) 1 : 2

(d) 1 : 4

Q995. In measuring the sides of a rectangle, there is an excess of 5% on one side and 2% deficit on the other. Then the error percent in the area is

(a) 3.3

(b) 3.0

(c) 2.9

(d) 2.7

Q996. A sphere and a cube have equal surface areas. The ratio of the volume of the sphere to that of the cube is

(a) √π : √6

(b) √6 : √π

(c)√2 : √π

(d)√π : 3

Q997. A circle and a square have equal areas. The ratio of a side of the square and the radius of the circle is

(a) 1 :√π

(b)√π : 1

(c) 1 : π

(d) π : 1

Q998. Surface areas of three adjacent faces of a cuboid are p, q, r. its volume is Q999. A copper wire, when bent in the form of a square encloses a region having area 121 cm2. If the same wire is bent in the form of a circle, then the area of the region enclosed by the wire will be [π = 22/7]

(a) 154 cm2

(b) 143 cm2

(c) 132 cm2

(d) 121 cm2

Q1000. A solid cone of height 9 cm with diameter of its base 18 cm is cut out from a wooden solid sphere of radius 9 cm. The percentage of wood wasted is:

(a) 25

(b) 30

(c) 50

(d) 75

Q1001. The area of an equilateral triangle is 4√3 cm2. The length of each side of the triangle is:

(a) 3 cm

(b) 2 cm

(c) 2 cm

(d) 4 cm

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