## Mensuration Part 8: Advance math series 2000 most important questions.

Mensuration Part 8: Advance math series 2000 most important question

**Q802. 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

**Q803. The area of the greatest circle inscribed inside a square of side 21 cm is **

**(taking π = 22/7 )**

(a) 344.5 cm^{2}

(b) 364.5 cm^{2}

(c) 346.5 cm^{2}

(d) 366.5 cm^{2}

**Q804.** **If the radius of a sphere is increased by 2 cm, its surface area increases by 252 cm ^{2}. The radius of the sphere before increase was (taking π = 22/7 )**

(a) 3 cm

(b) 4 cm

(c) 5 cm

(d) 6 cm

**Q805. 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

**Q806.** **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: (taking π = 22/7 )**

(a) 22 m

(b) 20 m

(c) 21 m

(d) 24 m

**Q807.** **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

**Q808. 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

**Q809.** **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, 33cm^{2}

(b) Circle, 33 cm^{2}

(c) Both have equal area

(d) Square, 495 cm^{2}

**Q810. 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) **

**(taking π = 22/7 )**** is nearly.**

(a) 3017.1

(b) 3170

(c) 301.7

(d) 30.17

**Q811. 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

**Q812. 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

(b) 8 cm

(d) 12.5 cm

**Q813. 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

**Q814. 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: (use π = 22/7 ) **

**Q815.** **The volume of a right circular cylinder whose height is 40 cm, and circumference of its base is 66 cm, is:**

(a) 55440 cm^{3}

(b) 3465 cm^{3}

(c) 7720 cm^{3}

(d) 13860 cm^{3}

**Q816. 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

**Q817. 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)

**Q818.** **A cone of height 7 cm and base radius 1 cm is carved from a cuboidal block of wood 10 cm x 5cm x 2cm. ****Assuming π = 22/7 **** the percentage wood wasted in the process is:**

**Q819.** **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) √32cm

(d) 8 cm

**Q820. 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 cm^{2}

(b) 216 cm^{2}

(c) 432 cm^{2}

(d) 108 cm^{2}

**Q821**. **If a wire is bent into the shape of a square, the area of the square is 81 sq. cm. When the wire is bent into a semicircular shape, the area of the semicircle (taking π = 22/7**** ) is:**

(a) 154 cm^{2}

(b) 77 cm^{2}

(c) 44 cm^{2}

(d) 22 cm^{2}

**Q822. Find the length of the longest rod that can be placed in a hall of 10 m length, 6 m breadth and 4 m height.**

**Q823.** **The areas of a square and a rectangle are equal. The length of the rectangle is greater than the length of any side of the square by 5 cm and the breadth is less by 3 cm. Find the perimeter of the rectangle.**

(a) 17 cm

(b) 26 cm

(c) 30 cm

(d) 34 cm

**Q824.** **The perimeter of the top of a rectangular table is 28m., whereas its area is 48m ^{2}. What is the length of its diagonal?**

(a) 5m.

(b) 10m.

(c) 12m.

(d) 12.5m.

**Q825.** **The length of a rectangular garden is 12 metres and its breadth is 5 metres. Find the length of the diagonal of a square garden having the same area as that of the rectangular garden:**

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**Q826.** **The base radii of two cylinders are in the ratio 2: 3 and their heights are in the ratio 5: 3. The ratio of their volumes is:**

(a) 27: 20

(b) 20: 27

(c) 9: 4

(d) 4: 9

**Q827.** **The slant height of a conical mountain is 2.5 km and the area of its base is 1.54 km ^{2}. Taking π = 22/7 **

**the height of the mountains is:**

(a) 2.2 km

(b) 2.4 km

(c) 3 km

(d) 3.11 km

**Q828.** **A solid metallic cone of height 10 cm, redius of base 20 cm is melted to make spherical balls each of 4 cm. Diameter. How many such balls can be made?**

(a) 25

(b) 75

(c) 50

(d) 125

**Q829.** **A hemisphere and a cone have equal bases. If their heights are also equal, the ratio of their curved surfaces will be:**

(a) 1:√2

(b) √2 : 1

(c) 1: 2

(d) 2: 1

**Q830.** **The diameter of a toy wheel is 14 cm. What is the distance travelled by it in 15 revolutions?**

(a) 880 cm

(b) 660 cm

(c) 600 cm

(d) 560 cm** **

**Q831. A wire when bent in the form of a square encloses an area of 484 sq. cm. What will bel the enclosed area when the same wire is bent into the form of a circle?(Take π = 22/7)**

(a) 462 sq.cm

(b) 539 sq. cm

(c) 616 sq.cm

(d) 693sq.cm

**Q832. What is the volume of a cube (in cubic cm) whose diagonal measures 4√3**** cm?**

(a) 16

(b) 27

(c) 64

(d) 8

**Q833. 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) 1 : 3

(d) 1 : 27

**Q834. The area of a circle is 38.5 sq. cm. Its circumference (in cm) is (use π = 22/7)**

(a) 22

(b) 24

(c) 26

(d) 32

**Q835. If the length of rectangle is increased by 25% and the width is decreased by 20%, then the area of the rectangle:**

(a) increases by 5%

(b) decrease by 5%

(c) remains unchanged

(d) increases by 10%

**Q836. The area of a circle of a radius 5 is numerically what percent of its circum-ference?**

(a) 200

(b) 225

(c) 240

(d) 250

**Q837. The radius of a wheel is 21 cm. how many revolution will it make in travelling 924 metres?**** (use = π = 22/7)**** **

(a) 7

(b) 11

(c) 200

(d) 700

**Q838. If the circumference of a circle increases from 4**** to 8 π****, what change occurs in its area?**

(a) It doubles.

(b) It triples

(c) It quadruples

(d) It is halved

**Q839. The perimeters of a square and a circular field are the same. If the area of the circular field is 3850 sq metres, what is the area (in m ^{2}) of the square?**

(a) 4225

(b) 3025

(c) 2500

(d) 2025

**Q840. The area of the ring between two concentric circles, whose circumferences are 88 cm and 132 cm, is:**

(a) 780 cm

(b) 770 cm

(c) 715 cm

(d) 660 cm

**Q841. **How many cubes, each of edge 3 cm, can be cut from a cube of edge 15 cm?

(a) 25

(b) 27

(c) 125

(d) 144

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