Mensuration Part 5: Advance math series 2000 most important questions.

Mensuration Part 5: Advance math series 2000 most important questions.

Mensuration Part 5: Advance math series 2000 most important questions.

Q681. If the height of a cylinder is increased by 15 per cent and the radius of its base is decreased by 10 percent then by what percent will its curved surface area change?

(a) 3.5 per cent decrease

(b) 3.5 per cent increase

(c) 5 per cent increase

(d) 5 per cent decrease

Q682. The base and altitude of a right angled triangle are 12 cm and 5 cm respectively. The perpendicular distance of its hypotenuse from the opposite vertex is

Q683. In right circular cone, the radius of its base is 7 cm and its height 24 cm. A cross-section is made through the midpoint of the height parallel to the base. The volume of the upper portion is

(a) 169 cm3

(b) 154 cm3

(c) 1078 cm3

(d) 800 cm3

Q684. A wire, bent in the form of a square, encloses an area of 484 cm2. If the same wire is bent so as to form a circle, then the area enclosed will be:

(a) 484 cm2

(b) 538  cm2

(c) 616 cm2

(d) 644 cm2

Q685. A cone of height 15 cm and base diameter 30 cm is carved out of a wooden sphere of radius 15 cm. The percentage of wasted wood is:

(a) 75%

(b) 50%

(c) 40%

(d) 25%

Q686. The area of the shaded region in the figure given below is

Q687. Find the diameter of a wheel that makes 113 revolutions to go 2 km 26 decameters.

(Taken P = 22/7)

Q688. A rectangular paper sheet of dimensions 22 cm  folded in the form of a cylinder along its length. What will be the volume of this cylinder?

(a) 460 cm3

(b) 462 cm3

(c) 624 cm3

(d) 400 cm3

Q689. By melting a solid lead sphere of diameter 12 cm, three small spheres are made whose diameters are in the ratio 3 : 4 : 5. The radius (in cm) of the smallest sphere is

(a) 3

(b) 6

(c) 1.5

(d) 4

Q690. The area of an equilateral triangle inscribed in a circle is 4 cm2. The area of the circle is

Q691. The ratio of the areas of the in-circle and the circum-circle of a square is

Q692. If the length of a rectangle is increased by 20% and its breadth is decreased by 20%, then its area

(a) increases by 4%

(b) decreases by 4%

(c) decreases by 1%

(d) remains unchanged

Q693. If the ratio of volumes of two cones is 2 : 3 and the ratio of the radii of their bases is 1 : 2, then the ratio of their heights will be

(a) 3 : 8

(b) 8 : 3

(c) 4 : 3

(d) 3 : 4

Q694. The volume of a cube (in cm3). Whose diagonal measures 4 cm is

(a) 16

(b) 27

(c) 64

(d) 8

Q695. If the height and the radius of the base of a cone are each increased by 100%, then the volume of the cone becomes

(a) double that of the original

(b) Three time that of the original

(c) six times that of the original

(d) eight times that of the original

Q696. In an isosceles triangle, the measure of each of equal sides is 10cm and the angle between them is 45, the area of the triangle is

Q697. A copper rod of 1 cm diameter and 8 cm length is drawn into a wire of uniform diameter and 18 m length. The radius (in cm) of the wire is

Q698. The area of circle whose radius is 6 cm is trisected by two concentric circles. The radius of      the smallest circle is

Q699. The ratio of the surface area of a sphere and the curved surface area of the cylinder circumscribing the sphere is

(a) 1 : 2

(b) 1 : 1

(c) 2 : 1

(d) 2 : 3

Q700. If the height of a right circular cone is increased by 200% and the radius of the base is reduced by 50%, the volume of the cone

(a) increases by 25%

(b) increases by 50%

(c) remains unaltered

(d) decreases by 25%

Q701. If the difference between the circumference and diameter of a circumference and diameter of a circle is 30 cm, then the radius of the circle must be

(a) 6 cm

(b) 7 cm

(c) 5 cm

(d) 8 cm

Q702. Some solid metallic right circular cones. Each with radius of the base 3 cm and height 4 cm, are melted to form a solid sphere of radius 6 cm. The number of right circular cones is

(a) 12

(b) 24

(c) 48

(d) 6

Q703. 12 spheres of the same size are made by melting a solid cylinder of 16 cm diameter and 2cm height. The diameter of each sphere is:

Q704. The diagonal of a square is 4 cm. The diagonal of another square, whose area is double that of the first square, is

(a) 8 cm

(b) 16 cm

(c)  cm

(d) 8 cm

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

(a) 12 cm

(b) 24 cm

(c) 18 cm

(d) 36 cm

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Q706. A wire when bent in the form of a square encloses an area of 484 sq cm. What will be the enclosed area when the same wire is bent into the form of a circle? (Taken π = 22/7)

(a) 462 sq cm.

(b) 539 sq cm.

(c) 616 sq cm.

(d) 693 sq cm.

Q707. A square and an equilateral triangle are drawn on the same base. The ratio of their areas is

Q708. The volume of cuboid is twice that 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

Q709. If the areas of a circle and a square are equal, then the ratio of their perimeters is

Q710. The number of revolutions, a wheel of diameter 40 cm makes in travelling in distance of 176 m, is (Taken π = 22/7)

(a) 140

(b) 150

(c) 160

(d) 166

Q711. The ratio of the volume of a cube to that of a sphere, which will fit exactly inside the cube, is

Q712. 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

Q713. The sum of radii of two spheres is 10 cm and the sum of their volumes is 880 cm3. What will be the product of their radii?

Q714. The circumference of a circle is 100 cm. The side of a square inscribed in the circle is

Q715. A circular wire of radius 42 cm is bent in the form of a rectangle whose sides are in the ratio of 6: 5. The smaller side of the rectangle is (Taken π = 22/7)

(a) 60 cm

(b) 30 cm

(c) 25 cm

(d) 36 cm

Q716. If the length and breadth of a rectangle are in the ratio 3 : 2 and its perimeter is 20 cm, then the area of the rectangle (in cm2) is:

(a) 24

(b) 48

(c) 72

(d) 96

Q717. The areas of a square and a rectangle are equal. The length of the rectangle is greater than the length of a side of the square by 5 cm and the breadth is less than the length of the side of the square by 3 cm. The perimeter of the rectangle is:

(a) 17 cm

(b) 26 cm

(c) 30 cm

(d) 34 cm

Q718. When the circumference of a toy ballon is increased from 20 cm to 25 cm, its radius (in cm) is increased by

(a)  5

(b) 5/π

(c) 5/2π

(d) π/5

Q719. The ratio of the area of a square to that of the square drawn on its diagonal is:

(a) 1 : 1

(b) 1 : 2

(c) 1 : 3

(d)1 : 4

Q720. 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

Q721. The surface area of a sphere is 64cm2. Its diameter is equal to

(a) 16 cm

(b) 8 cm

(c) 4 cm

(d) 2 cm