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Mensuration Part 10: Advance math series 2000 most Important Questions.

Mensuration Part 10: Advance math series 2000 most important question:- Q882. The heights of two cones are in the ratio 1 : 3 and the diameters of their bases are in the ratio 3 : 5. The ratio of their volumes is

(a) 3 : 25

(b) 4 : 25

(c) 6 : 25

(d) 7 : 25

Q883. A solid hemisphere is of radius 11 cm. The curved surface area in sq. cm is

(a) 1140.85

(b) 1386.00

(c) 760.57

(d) 860.5

Q884. A circle is inscribed in a square whose length of the diagonal is 12√2 cm. An equilateral triangle is inscribed in that circle. The length of the side of the triangle is

(a) 4√3 cm

(b) 8√3 cm

(c) 6√3 cm

(d) 11√3 cm

Q885. What is the area of the triangle whose sides are 9cm, 10cm and 11cm?

(a) 30 cm2

(b) 60 cm2

(c) 30√2 cm2

(d) 60√2 cm2

Q886. The internal radius and thickness of a hollow metallic pipe are 24 cm and 1 cm respectively. It is melted and recast into a solid cylinder of equal length. The diameter of the solid cylinder will be

(a) 7 cm

(b) 14 cm

(c) 10 cm

(d) 5 cm

Q887. If the length of each median of an equilateral triangle is 6√3 cm, the perimeter of the triangle is

(a) 24 cm

(b) 32 cm

(c) 36 cm

(d) 42 cm

Q888. The radius of a metallic cylinder is 3 cm and its height is 5 cm. It is melted and moulded into small cones, each of height 1 cm and base radius 1 mm, The number of such cones formed, is

(a) 450

(b) 1350

(c) 8500

(d) 13500

Q889. A gear 12 cm in diameter is turning a gear 18 cm in diameter. When the smaller gear has 42 revolutions, how many has the larger on made?

(a) 28

(b) 20

(c) 15

(d) 24

Q890. The ratio of sides of a triangle is 3 : 4 : 5 and area of the triangle is 72 square unit. Then the area of an equilateral triangle whose perimeter is same as that of the previous triangle is

(a) 32√3 square unit

(b) 48√3 square unit

(c) 96 square unit

(d) 60√3 square unit

Q891. The adjacent sides of a parallelogram are 36 cm and 27 cm in length. If the distance between the shorter sides is 12 cm, then the distance between the longer sides is

(a) 10 cm

(b) 12 cm

(c) 16 cm

(d) 9 cm

Q892. The length and perimeter of a rectangle are in the ratio 5 : 18. Then length and breadth will be in the ratio

(a) 4 : 3

(b) 3 : 5

(c) 5 : 4

(d) 4 : 7

Q893. The radii of the base of a cylinder and a cone are in the ratio √3 : √2 and their heights are in the ratio √2  : √3 . Their volumes are in the ratio of

(a) √3 : √2

(b) 3 √3:√2

(c) √3 : 2√2

(d) √2 : √6

Q894. The radius and height of a cylinder are in the ratio. 5 : 7 and its volume is 550 cm3. Calculate its curved surface area in sq.cm.

(a) 110

(b) 444

(c) 220

(d) 616

Q895. The area of an isosceles triangle is 4 square unit. If the length of the third side is 2 unit, the length of each equal side is

(a) 4 unit

(b) 2√3 unit

(c) √17 unit

(d) 3 √2 unit

Q896. A right circular cylinder and a sphere have same radius and same volume. The ratio of their surface area is

(a) 8 : 3

(b) 9 : 4

(c) 4 : 3

(d) 7 : 6

Q897. The radii of two circles are 5 cm and 12 cm. The area of a third circle is equal to the sum of the areas of the two circles. The radius of the third circle is:

(a) 13 cm

(b) 21 cm

(c) 30 cm

(d) 17 cm

Q898. A sphere and a hemisphere have the same volume. The ratio of their radii is

(a) 1 : 2

(b) 1 : 8

(c) 1 : √2

(d) 1 : 3√2

Q899. If two adjacent sides of a rectangular parallelepiped are 1 cm and 2 cm and the total surface area of the parallelepiped is 22 square cm, then the diagonal of the parallelepiped is

(a)  √10 cm

(b) 2 √3 cm

(c) √14 cm

(d) 4 cm

Q900. The ratio of sides of a triangle is 3 : 4 : 5. If area of the triangle is 72 square units, then the length of the smallest side is:

(a) 4 √3 unit

(b) 5 √3 unit

(c) 6 √3  unit

(d) 3 √3 unit

Q901. The area of the curved surface and the area of the base of a right circular cylinder are a square cm and b square cm respectively. The height of the cylinder is

(a)  2a/√πbcm

(b) a√b/2√π  cm

(c) a/2√πb  cm

(d) a√π/2b cm

Q902. If the radius of a sphere be doubled, the area of its surface will become

(a) Double

(b) Three times

(c) Four times

(d) none of mentioned

Q903. The edges of a rectangular box are in the ratio 1 : 2 : 3 and its surface area is 88 cm2. The volume of the box is

(a) 24 cm3

(b) 48 cm3

(c) 64 cm3

(D) 120 cm3

Q904. The maximum length of a pencil that can be kept in a rectangular box of dimensions 8 cm  × 6 cm × 2 cm is

(a) 2√13 cm

(b) 2√14 cm

(c) 2√26 cm

(d) 10 √2cm

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Q905. If the surface area of two spheres are in the ratio 4 : 9, then the ratio of their volumes will be:

(a) 16 : 81

(b) 2 : 3

(c) 4 : 9

(d) 8 : 27

Q906. The diameter of the moon is assumed to be one fourth of the diameter of the earth. The the ratio of the volume of the earth to that of the moon is

(a) 64 : 1

(b) 1 : 64

(c) 60 : 7

(d) 7 : 60

Q907. A parallelepiped whose sides are in ratio 2 : 4 : 8 have the same volume as a cube. The ratio of their surface area is:

(a) 7 : 5

(b) 4 : 3                                    `

(c) 8 : 5

(d) 7 : 6

Q908. If the slant height of aright pyramid with square base is 4 metre and the total slant surface of the pyramid is 12 square metre, then the ratio of total slant surface and area of the base is:

(a) 16 : 3

(b) 24 : 5

(c) 32 : 9

(d) 12 : 3

Q909. If the length of each side of an equilateral triangle is increased by 2 unit, the area is found to be increased by 3 +√3 square unit. The length of each side of the triangle is

(a) √3 unit

(b) 3 unit

(c) 3√3 unit

(d) 1 + 3√3 unit

Q910. The area of a circle is increased by 22 cm2 when its radius is increased by 1 cm. The original radius of the circle is

(a) 3 cm

(b) 5 cm

(c) 7 cm

(d) 9 cm

Q911. The base of a right circular cone has the same radius a as that of a sphere. Both the sphere and the cone have the same volume. Height of the cone is

(a) 3a

(b) 4a

(c)7/4 a

(d)7/3 a

Q912. A hemispherical cup of radius 4 cm is filled to the brim with coffee. The coffee is then poured into a vertical cone of radius 8cm and height 16 cm. The percentage of the volume of the cone that remains empty is:

(a) 87.5%

(b) 80.5%

(c) 81.6%

(d) 88.2%

Q913. If a solid cone of volume 27 π cm3 is kept inside a hollow cylinder whose radius and height are that of the cone, then the volume of water needed to fill the empty space is

(a) 3π cm3

(b) 18π cm3

(c) 54 π cm3

(d) 81 π cm3

Q914 The parallel sides of a trapezium are in a ratio 2 : 3 and their shortest distance is 12 cm. if the area of the trapezium is 480 sq.cm., the longer of the parallel sides is of length:

(a) 56 cm

(b) 36 cm

(c) 42 cm

(d) 48 cm

Q915. A sphere and a hemisphere have the same volume. The ratio of their curved surface areas is:

(a) 2-3/2 : 1

(b)2-2/3  : 1

(c)  4-2/3 : 1

(d) 2 1/3 : 1

Q916. The lengths of three medians of a triangle are 9 cm, 12 cm and 15 cm. The area (in sq.cm) of the triangle is

(a) 24

(b) 72

(c) 48

(d) 144

Q917. The height of a right prism with a square base is 15 cm. If the area of the total surfaces of the prism is 608 sq. its volume is

(a) 910 cm3

(b) 920 cm3

(c) 960 cm3

(d) 980 cm3

Q918. If the diagonals of a rhombus are 8 and 6, then the square of its size is

(a) 25

(b) 55

(c) 64

(d) 36

919. The area of the square inscribed in a circle of radius 8 cm is

(a) 256 sq.cm

(b) 250 sq.cm

(c) 128 sq.cm

(d) 125 sq.cm

Q 920.The base of a cone and a cylinder have the same radius 6 cm; they have also the same height 8 cm. The ratio of the curved surfaces of the cylinder to that of the cone is

(a) 8 : 5

(b) 8 : 3

(c) 4 : 3

(d) 5 : 3

Q921. A cone and a hemisphere stand on equal base and have the same height. The ratio of their whole surfaces is

(a) √2 + 1 : 3

(b) √2 – 1 : 3

(c)√2  : 3

(d) 2 : 3 Maths