## Mensuration Part 11: Advance Math Series 2000 Most Important Questions.

Mensuration Part 11: Advance Math Series 2000 Most Important Questions.

**Q922. From a solid cylinder whose height is 12 cm and diameter 10 cm, a conical cavity of same height and same diameter of the base is hollowed out. The volume of the remaining solid is approximately (π = 22/7)**

(a) 942.86 cm^{3}

(b) 314.29 cm^{3}

(c) 628.57 cm^{3}

(d) 450.76 cm^{3}

**Q923. The base of a right pyramid is a square of side 40 cm long. If the volume of the pyramid is 8000 cm ^{3}, then its height is:**

(a) 5 cm

(b) 10 cm

(c) 15 cm

(d) 20 cm

**Q924. The ratio of length of each equal side and the third side of an isosceles triangles is 3 : 4. If the area of the triangle is 18√5**** square unit, the third side is**

(a) 16 unit

(b) 5**√10** unit

(c) 8**√2** unit

(d) 12 unit

**Q925. The perimeter of a rhombus is 100 cm. If one of its diagonals is 14 cm, then the area of the rhombus is**

(a) 144 cm^{2}

(b) 225 cm^{2}

(c) 336 cm^{2}

(d) 400 cm^{2}

**Q926. The radius of the base of a right circular cone is doubled. To keep to volume fixed, the height of the cone will be**

(a) one-fourth of the previous height

(b) times of the previous height

(c) half of the previous height

(d) one-third of the previous height

**Q270. The radius of a cylinder is 10 cm and height is 4 cm. The number of centimeters that may be added either to the radius or to the height to get the same increase in the volume of the cylinder is**

(a) 5

(b) 4

(c) 25

(d) 16

**Q927. The length of a room floor exceeds its breadth by 20 m. The area of the floor remains unaltered when the length is decreased by 10 m but the breadth is increased by 5m. The area of the floor (in square metres) is:**

(a) 280

(b) 325

(c) 300

(d) 420

**Q928. The base of a right pyramid is a square of side 16 cm long. If its height be 15 cm, then the area of the lateral surface in square centimeter is:**

(a) 136

(b) 544

(c) 800

(d) 1280

**Q929. A semicircular shaped window has diameter of 63 cm. Its perimeter equals (π = 22/7)**

(a) 126 cm

(b) 162 cm

(c) 198 cm

(d) 251 cm

**Q930. A parallelogram ABCD has sides AB = 24 cm and AD = 16 cm. The distance between the sides AB and DC is 10 cm. Find the distance between the sides AD and BC.**

(a) 16 cm.

(b) 18 cm.

(c) 15 cm.

(d) 26 cm.

**Q931. From a right circular cylinder of radius 10 cm and height 21 cm, a right circular cone of same base-radius is removed. It the volume of the remaining portion is 4400 cm ^{3}, then the height of the removed cone (Take π = 22/7)**

(a) 15 cm

(b) 18 cm

(c) 21 cm

(d) 24cm

**Q932. A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. The area of the circle is [Take π = 22/7]**

(a) 125 cm^{2}

(b) 230 cm^{2}

(c) 550 cm^{2}

(d) 616 cm^{2}

**Q933. A street of width 10 metres surrounds from outside a rectangular garden whose measurement is 200m **** 180m. The area of the path (in square metres) is**

(a) 8000

(b) 7000

(c) 7500

(d) 8200

**Q934. The height of a circular cylinder is increased six times and the base area is decreased tone-ninth of its value. The factor by which the lateral surface of the cylinder increases is**

(a) 2

(b)1/2

(c)2/3

(d)3/2

**Q935. From a solid cylinder of height 10 cm and radius of the base 6 cm, a cone of same height and same base is removed. The volume of the remaining solid is:**

(a) 240 cu.cm

(b) 5280 cu.cm

(c) 620 cu.cm

(d) 360 cu.cm

**Q936. A cylindrical can whose base is horizontal and is of internal radius 3.5 cm contains sufficient water so that when a solid sphere is placed inside, water just covers the sphere. The sphere fits in the can exactly. The depth of water in the can before the sphere was put is**

(a) 35/3 cm

(b) 17/3 cm

(c) 7/3 cm

(d) 14/3 cm

**Q937. A playground is in the shape of a rectangle. A sum of Rs. 1,000 was spent to make the ground usable at the rate of 25 paise per sq.cm. The breadth of the ground is 50m. If the length of the ground is increased by 20m, what will be the expenditure in rupees at the same rate per sq.m.?**

(a) 1,250

(b) 1,000

(c) 1,500

(d) 2,250

**Q938. Two can of rain has fallen on a square km of land. Assuming that 50% of the raindrops could tained in a pool having a 100 m **** 10 m base, by what level would the water level in the pool have increased?**

(a) 1 km

(b) 10 m

(c) 10 cm

(d) 1 m

**Q939. The number of spherical bullets that can be made out of a solid cube of lead whose edge measures 44 cm, each bullet being of 4 cm diameter, is (Take π = 22/7)**

(a) 2541

(b) 2451

(c) 2514

(d) 2415

**Q940. The height of a solid right circular cylinder is 6 metres and three times the sum of the areas of its two end faces is twice the area of its curved surface. The radius of its base, in metre, is**

(a) 4

(b) 2

(c) 8

(d) 10

**Q941. A semi-circular sheet of metal of diameter 28 cm is bent into an open conical cup. The depth of the cup is approximately**

(a) 11 cm

(b) 12 cm

(c) 13 cm

(d) 14 cm

**Q942. The diameter of a cylinder is 7 cm and its height is 16 cm. using the value of π**** =22/7 ****, the lateral surface area of the cylinder is**

(a) 352 cm^{2}

(b) 350 cm^{2}

(c) 355 cm^{2}

(d) 348 cm^{2}

**Q943. The ratio of the areas of the circumcircle and the incircle a square is:**

(a) 2 : 1

(b) √ 2: 1

(c)√2 : √3

(d) √3 : 1

**Q944. A hall is 15 metre long and 12 metre broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of the four walls, the volume of the hall, in cubic metre, is**

(a) 720

(b) 900

(c) 1200

(d) 1800

**Q945. If the four equal circles of radius 3 cm touch each other externally, then the area of the region bounded by the four circles is**

(a) 4(9 –π) sq.cm

(b) 9(4 –π)sq.cm

(c) 5(6 –π)sq.cm

(d) 6(5 –π) sq.cm

**Q946. The areas of curved surface of a right circular cylinder and a sphere are equal. If the radii of the cylinder and the sphere be equal, then the ratio of their volumes will be**

(a) 2 : 3

(b) 3 : 2

(c) 3 : 4

(d) 4 : 3

**Q947. Sides of a parallelogram are in the ratio 5 : 4. Its area is 1000 sq. units. Altitude on the greater side is 20 units. Altitude on the smaller side is**

(a) 30 units

(b) 25 units

(c) 10 units

(d) 15 units

**Q948. A right angled sector of radius r cm is rolled up into a cone in such a way that the two binding radii are joined together. Then the curved surface area of the cone is**

(a) πr^{2} cm^{2}

(b) 4πr^{2} cm^{2}

(c) πr^{2}/4 cm^{2}

(d) 2 πr^{2} cm^{2}

**Q949. in a triangular field having sides 30m, 72m and 78m, the length of the altitude to the side measuring 72m is:**

(a) 25 m

(b) 28 m

(c) 30 m

(d) 35 m

**Q950. The perimeter of a triangle is 40 cm and its area is 60 cm ^{2}. If the largest side measures 17 cm, then the length (in cm) of the smallest side of the triangle is**

(a) 4

(b) 6

(c) 8

(d) 15

**Q951. If the length of each side of a regular tetrahedron is 12 cm, then the volume of the tetrahedron is**

(a) 144 cu. cm.

(b) 72 cu. cm.

(c) 8 cu. cm.

(d) 12 cu. cm.

**Q952. The base of a right prism is a trapezium. The lengths of the parallel sides are 8 cm and 14cm and the distance between the parallel sides is 8 cm. If the volume of the prism is 1056 cm ^{3}, then the height of the prism is**

(a) 44 cm

(b) 16.5 cm

(c) 12cm

(d) 10.56 cm

**Q953. A right circular cylinder and a cone have equal heights. It their curved surfaces are in the ratio 8 : 5, then the radius of the base to the height are in the ratio:**

(a) 2 : 3

(b) 3 : 4

(c) 3 : 4

(d) 3 : 2

**Q954. A metal pipe is 21 cm long and its exterior diameter is 8 cm. If the thickness of the pipe is 1cm and the metal weighs8 gm/cm ^{3}, the weight of the pipe (in kg.) is(Take π = 22/7)**

(a) 3.696

(b) 3.669

(c) 3.966

(d) 3.699

**Q956. The ratio of height and the diameter of a right circular cone is 3 : 2 and its volume is 1078 cc, then (Take π = 22/7)**** its height is:**

(a) 7 cm

(b) 14 cm

(c) 21 cm

(d) 28 cm

**Q957. The ratio of the areas of the incircle and the circumcircle of a square is:**

(a) 1 : 2

(b) 2 : 3

(c) 3 : 4

(d) 4 : 5

**Q958. A circus tent is cylindrical up to a height of 3 m and conical above it. If its diameter is 105 m and the slant height of the conical part is 63 m, then the total area of the canvas required to make the tent is(Take π = 22/7) **

(a) 11385 m^{2}

(b) 10395 m^{2}

(c) 9900 m^{2 }

(d) 990 m^{2}

**Q959. A metal wire when bent in the form of a square encloses an area 484 cm ^{2}. If the same wire is bent in the form of a circle, then(Take π = 22/7) **

**its area is**

(a) 308 cm^{2}

(b) 506 cm^{2}

(c) 600 cm^{2}

(d) 616 cm^{2}

**Q960. If A denotes the volume of a right circular cylinder of same height as its diameter, and b is the volume of a sphere of same radius, then A/B **** is:**

(a) 4/3

(b) 3/2

(c) 2/3

(d) 3/4

**Q961. The radius and the height of a cone are in the ratio 4 : 3. The ratio of the curved surface area and total surface area of the cone is**

(a) 5 : 9

(b) 3 : 7

(c) 5 : 4

(d) 16 : 9

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