Introduction to Mensuration

Q. Question 3
The base of an isosceles triangle is $\frac{4}{3}cm$. The perimeter of the triangle is $4\frac{2}{15}cm$. What is the length of either of the remaining equal sides?

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 $\frac{32}{9}cm$. The diameter of the cylindrical vessel is _____.

1. $12cm$
2. $14cm$
3. $16cm$
4. $18cm$

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

1. $\pi h^2$
2. $\frac{4}{3}\pi h^2$
3. $\frac{3}{2}\pi h^2$
4. $2\pi h^2$

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?

1. $455sq.cm$

2. $154sq.cm$

3. $301sq.cm$

4. $509sq.cm$

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 $\frac{32}{9}cm$.

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.

1. 97.75 cm²

2. 98.12 cm²

3. 100.57 cm²

4. 94.54 cm²

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 ${cm}^2$of the shaded region. [1 MARK]

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.

The point of intersection of ___ bisectors of all the sides of a triangle is called circumcentre.

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?

1. r²/4

2. 2r²

3. r²

4. r²/2

Q.

In a triangle ABC, O is the center of incircle PQR, $\angle$BAC = ${65}^{\circ }$, $\angle$BCA = ${75}^{\circ }$, find $\angle$ ROQ:

1. 80°

2. 120°

3. 140°

4. 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 = $\frac{1}{2}\times \text{height}\times$ sum of ___ sides.

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 $—$ the original volume if its radius becomes half the original radius .

Q.

A jar containing $2695c{m}^3$ of juice is used to fill smaller hemispherical bowls having radius 3.5 cm. Find the number of bowls that can be filled.

1. 8

2. 10

3. 30

4. 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

1. $4.5cm$
2. $4cm$
3. $3cm$
4. $2cm$

Q. A cubical block of side $7cm$ 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

1. 90 degrees

2. 45 degrees

3. 60 degrees

4. 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?

1. 97.75 $c{m}^2$

2. 94.54$c{m}^2$

3. 98.12 $c{m}^2$

4. 100.57 $c{m}^2$

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:

1. 2.5 cm

2. 4 cm

3. 6 cm

4. 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 $\pi$ = $3$)

1. $2520$ $c{m}^2$
2. $2420$ $c{m}^2$
3. $2220$ $c{m}^2$
4. $2120$ $c{m}^2$

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?

1. 97.75 $c{m}^2$

2. 94.54$c{m}^2$

3. 98.12 $c{m}^2$

4. 100.57 $c{m}^2$

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.

1. 97.75 cm²

2. 94.54 cm²

3. 98.12 cm²

4. 100.57 cm²

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

1. ${90}^{\circ }$
2. ${45}^{\circ }$
3. ${60}^{\circ }$
4. ${30}^{\circ }$

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

1. $3cm$
2. $6cm$
3. $4cm$
4. $5cm$

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 $9\frac{1}{3}$ cm. Find the diameter of the base of the cylinder.

1. $12$ cm
2. $16$ cm
3. $18$ cm
4. $14$ cm

Q. The area of the black region is $100(\pi -2)unit{s}^2$. Calculate the diameter of the circle.