# Introduction to Mensuration

## Trending Questions

**Q.**Question 3

The base of an isosceles triangle is 43cm. The perimeter of the triangle is 4215cm. What is the length of either of the remaining equal sides?

**Q.**A sphere of diameter 12 cm, is dropped in a right circular cylindrical vessel, partly filled with water. If the sphere is completely submerged in water, the water level in the cylindrical vessel rises by 329 cm. The diameter of the cylindrical vessel is _____.

- 12 cm
- 14 cm
- 16 cm
- 18 cm

**Q.**If the diameter of the base of a closed right circular cylinder be equal to its height h, then its total surface area is

- πh2
- 43πh2
- 32πh2
- 2πh2

**Q.**

In the given figure, a circle is inscribed in a trapezium of height 14 cm and lengths of parallel sides are equal to 25 cm and 40 cm. What is the area of the shaded region?

455 sq.cm

154 sq.cm

301 sq.cm

509 sq.cm

**Q.**A sphere of diameter 12 cm, is dropped in a right circular cylindrical vessel, partly filled with water. If the sphere is completely submerged in water, the water level in the cylindrical vessel rises by 329cm.

Find the diameter of the cylindrical vessel.

**Q.**

The Yin-Yang symbol can be explained with the following dimensions. What would be area covered by the Yin (black) region? The radius of the larger circle is, R = 8 cm.

97.75 cm

^{2}98.12 cm

^{2}100.57 cm

^{2}94.54 cm

^{2}

**Q.**

In the given figure, areas have been drawn of radius 21 cm each with vertices A, B, C, and D of quadrilateral ABCD as centres. Find the area in cm2of the shaded region. [1 MARK]

**Q.**A sphere of diameter 12 cm, is dropped in a right circular cylindrical vessel, partly filled with water. If the sphere is completely submerged in water, the water level in the cylindrical vessel rises by 359 cm. Find the diameter of the cylindrical vessel.

**Q.**

The point of intersection of

**Q.**

In the diagram, a square is drawn such that the diagonally opposite corners touch the Centre and the circumference of a circle with radius, r. what is the area of the of the square?

r

^{2}/42r

^{2}r

^{2}r

^{2}/2

**Q.**

In a triangle ABC, O is the center of incircle PQR, ∠BAC = 65∘, ∠BCA = 75∘, find ∠ ROQ:

80°

120°

140°

Can't be determined

**Q.**

**Find the surface area of the regular pyramid.**

**Q.**

A sphere of diameter $12cm,$ is dropped in a right circular cylindrical vessel, partly filled with water. If the sphere is completely submerged in water, the water level in the cylindrical vessel rises by $3\frac{5}{9}cm.$. Find the diameter of the cylindrical vessel.

**Q.**

Area of a trapezium = 12×height× sum of

**Q.**Find the area of the shaded region in Fig., if ABCD is a square of side 14cm and APD and BPC are semicircles.

**Q.**

The volume of a cylinder becomes $\u2014$ the original volume if its radius becomes half the original radius .

**Q.**

A jar containing 2695 cm3 of juice is used to fill smaller hemispherical bowls having radius 3.5 cm. Find the number of bowls that can be filled.

8

10

30

15

**Q.**A sphere of radius 6cm is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is 8cm. If the sphere is Submerged completely, then the surface of the water rises by

- 4.5cm
- 4cm
- 3cm
- 2cm

**Q.**A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.

**Q.**

The angle subtended by the diameter of a circle is

90 degrees

45 degrees

60 degrees

180 degrees

**Q.**

The Yin-Yang symbol can be explained by the following dimensions. What would be the area covered by the Yin (black) region if the radius of the larger circle is, R = 8 cm?

97.75 cm2

94.54cm2

98.12 cm2

100.57 cm2

**Q.**

The radii of two cylinders are in the ratio$2:3$and their heights are in the ratio$5:3$. Find the ratio of their volumes and ratios of their curved surfaces.

**Q.**

If a sector of radius 8cm with central 120⁰ is folded into a cone, the slant height of cone is:

2.5 cm

4 cm

6 cm

8 cm

**Q.**

If the radii of the circular ends of a conical glass are 15 and 9 cm whose slant height is 35 cm. Find the surface area of the glass? (Use π = 3)

- 2520 cm2
- 2420 cm2
- 2220 cm2
- 2120 cm2

**Q.**

The Yin-Yang symbol can be explained by the following dimensions. What would be the area covered by the Yin (black) region if the radius of the larger circle is, R = 8 cm?

97.75 cm2

94.54cm2

98.12 cm2

100.57 cm2

**Q.**

The Yin-Yang symbol can be explained with the following dimensions. What would be area covered by the Yin (black) region. The radius of the larger circle is, R=8 cm.

97.75 cm

^{2}94.54 cm

^{2}98.12 cm

^{2}100.57 cm

^{2}

**Q.**What will be the angle in each sector of the triangle if all the circles have equal radius?

- 90∘
- 45∘
- 60∘
- 30∘

**Q.**A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged then the water level rises by___.

- 3 cm
- 6 cm
- 4 cm
- 5 cm

**Q.**The internal and external radii of a metallic spherical shell are 4 cm and 8 cm, respectively. It is melted and recast into a solid right circular cylinder of height 913 cm. Find the diameter of the base of the cylinder.

- 12 cm
- 16 cm
- 18 cm
- 14 cm

**Q.**The area of the black region is 100(π−2)units2. Calculate the diameter of the circle.