## 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 cm^{3}

(b) 154 cm^{3}

(c) 1078 cm^{3 }

(d) 800 cm^{3}

**Q684. A wire, bent in the form of a square, encloses an area of 484 cm ^{2}. If the same wire is bent so as to form a circle, then the area enclosed will be: **

(a) 484 cm^{2}

(b) 538 cm^{2}

(c) 616 cm^{2}

(d) 644 cm^{2}

**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 cm^{3}

(b) 462 cm^{3}

(c) 624 cm^{3}

(d) 400 cm^{3}

**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**** cm ^{2}. 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 cm ^{3}). 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 cm^{2}

(b) 216 cm^{2}

(c) 432 cm^{2}

(d) 108 cm^{2}

**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 cm ^{3}. 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 cm ^{2}) 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 64cm ^{2}. Its diameter is equal to**

(a) 16 cm

(b) 8 cm

(c) 4 cm

(d) 2 cm

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