Free Printable Area Related to Circles & Surface area and Volumes

1.

The area of the circle is $49\pi\ cm^{2\ }$ . Its Circumference is

a)

$7\pi\ cm$

b)

$14\pi\ cm$

c)

$21\pi\ cm$

d)

$28\pi\ cm$

2.

Find the angle through which the minute hand of a clock moves from 6 p.m. to 6.35 p.m.

a)

90 degrees

b)

210 degrees

c)

180 degrees

d)

60 degrees

3.

The minute hand of a clock is of length 4cm. Find the angle swept by the minute hand in 15 minutes.

a)

$30\degree$

b)

$60\degree$

c)

$90\degree$

d)

$45\degree$

4.

Find the length of the arc in the given figure.

a)

11cm

b)

22cm

c)

33cm

d)

44cm

5.

The area of a quadrant of a circle with circumference of 44cm is........

a)

$77cm^{2\ }$

b)

$38.5cm^{2\ }$

c)

$35.5cm^{2\ }$

d)

$38cm^{2\ }$

6.

In a circle of radius 7cm, an arc subtends an angle of $30\degree$ at the centre, the length of the arc is:

a)

44cm

b)

28cm

c)

11/3 cm

d)

22/3 cm

7.

What will be the area swept by the hour hand of a clock is 8 hours, if the length of hour hand is 7cm?

a)

$\frac{112}{7}cm^{2\ }$

b)

$\frac{308}{3}cm^{2\ }$

c)

$\frac{191}{3}cm^{2\ }$

d)

$\frac{352}{3}cm^{2\ }$

8.

What is the area of the sector forming the region with the angle $210\degree$ and radius 28cm?

a)

$\frac{2478}{3}cm^{2\ }$

b)

$\frac{1179}{2}cm^{2\ }$

c)

$\frac{4312}{3}cm^{2\ }$

d)

$\frac{1159}{3}cm^{2\ }$

9.

The area of the segment of a circle with radius equal to 7cm and central angle of $60\degree$

a)

$3.14cm^{2\ }$

b)

$7.96cm^{2\ }$

c)

$4.29\ cm^{2\ }$

d)

$4.84cm^{2\ }$

10.

Which of the following can`t be the central angle of a major sector?

a)

180 degrees

b)

90 degrees

c)

360 degrees

d)

270 degrees

11.

If a larger pizza is divided into 8 equal sectors, then what will be the central angle of each sector?

a)

60 degrees

b)

30 degrees

c)

45 degrees

d)

90 degrees

12.

A sector has an area of $30\pi$ sq units and a central angle of $72\degree$ , find the radius of the circle.

a)

$5\sqrt[]{6}$

b)

$3\sqrt[]{7}$

c)

$6\sqrt[]{5}\ units$

d)

$2\sqrt[]{5}\ units$

13.

Determine the area of a sector with center angle $150\degree$ and a radius of 6 units

a)

$15\pi$

b)

$20\pi$

c)

$22\pi$

d)

$44\pi$

14.

In making 1000 revolutions, a wheel covers 88km. The diameter of the wheel is

a)

14m

b)

24m

c)

28m

d)

40m

15.

The radius of a wheel is 0.25m. How many revolutions will it make in covering 11km?

a)

2800

b)

4000

c)

5500

d)

7000

16.

The area of two circles are in the ratio 9:4. The ratio of their circumference is

a)

4:9

b)

2:3

c)

3:2

d)

9:4

17.

Assertion(A): Area of a sector of a circle with central angle of $90\degree$ is half of the area of the circle

Reason (R): The area of a sector of a circle is given by the formula $\frac{\theta}{360}\times\pi r^{2\ }$

a)

Both (A) and (R) are true and (R) is the correct explanation of (A)

b)

Both (A) and (R) are true and (R) is not the correct explanation of (A)

c)

(A) is true but (R) is false

d)

(A) is false but (R) is true

18.

If the circumference of a circle and the perimeter of a square are equal then

a)

area of the circle = area of the square

b)

(area of the circle)>(area of the square)

c)

(area of the circle)<(area of the square)

d)

none of these

19.

Assertion(A): The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24cm and 7cm is 50cm

Reason(R): If the perimeter and the area of a circle are numerically equal, then the radius of the circle is 2 units

a)

The assertion is false but the reason is true

b)

The assertion is true but the reason is false

c)

Both A and R are true and R is the correct explanation of A

d)

Both A and R are true and R is not the correct explanation of A

20.

Assertion(A): If circumferences of two circles are equal, then their areas will be equal

Reason(R): If the areas of two circles are equal, then their circumferences are equal

a)

Both (A) and (R) are true and Reason (R)is the correct explanation of Assertion (A)

b)

Both (A) and (R) are true and Reason (R)is not the correct explanation of Assertion (A)

c)

Assertion (A) is true but Reason (R)is false

d)

Assertion (A) is false but Reason (R)is true

21.

If a cone is surmounted on a hemisphere of radius r and height of the cone is equal to the diameter of the hemisphere, then what is the slant height of the cone ?

a)

$2r$

b)

$4r$

c)

$\sqrt[]{3}\ r$

d)

$\sqrt[]{5}\ r$

22.

A toy is in the form of a cone mounted on a hemisphere with same radius. The diameter of the base of the conical portion is 6cm and its height is 4cm. Surface area of the toy is:

a)

$36\pi\ cm^{2\ }$

b)

$33\pi\ cm^{2\ }$

c)

$35\pi\ cm^{2\ }$

d)

$24\pi\ cm^{2\ }$

23.

A cone with radius 5cm and slant height 13cm is placed on top of a hemisphere of radius 5 cm.

What is the TSA of the combination?

a)

$115\ \pi\ cm^{2\ }$

b)

$130\ \pi\ cm^{2\ }$

c)

$148\ \pi\ cm^{2\ }$

d)

$190\ \pi\ cm^{2\ }$

24.

If a cylinder is covered by two hemisphere shaped lid of equal size, then the total curved surface area of the new object will be:

a)

$4\pi rh\ +\ 2\pi r^{2\ }$

b)

$4\pi rh\ -\ 2\pi r^{2\ }$

c)

$2\pi rh\ +\ 4\pi r^{2\ }$

d)

$2\pi rh\ +\ 4\pi r^{\ }$

25.

A circus tent is cylindrical to a height of 4m and conical above. If its diameter is 105m and its slant height is 40m, then the total area of the canvas required in $m^{2\ }$ is

a)

1760

b)

2640

c)

3960

d)

7920

26.

Three cubes each of volume $216cm^2$ are joined end to end, then the volume of the resulting solid is

a)

$913cm^3$

b)

$414cm^3$

c)

$648cm^3$

d)

$242cm^3$

27.

A cylinder with radius 4cm and height 12cm is combined with a hemisphere of the same radius.

The total volume of the combination is:

a)

$\frac{704}{3}\pi\ cm^3$

b)

$\frac{112}{9}\pi\ cm^3$

c)

$304\pi\ cm^3$

d)

$\frac{200}{4}\pi\ cm^3$

28.

Find the volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm.

a)

$19.4cm^3$

b)

$16.4cm^3$

c)

$14.9cm^3$

d)

$9.4cm^3$

29.

A cone of volume $22cm^{3\ }$ is surmounted on the hemisphere of same radius and volume $15cm^3$ ,

then what is the volume of the solid?

a)

$37cm^3$

b)

$27cm^3$

c)

$57cm^3$

d)

$22cm^3$

30.

From a solid cube of side 7cm, a conical cavity of height 7cm and radius 3cm is hollowed out. Find the volume of remaining solid

a)

$277cm^3$

b)

$343cm^3$

c)

$409cm^3$

d)

$66cm^3$

31.

Assertion (A): From a solid cylinder whose height is 12cm and diameter is 10cm, a conical cavity of same height and the same diameter is hollowed out, Volume of the cone is $100\pi\ cm^3$

Reason (R): If a conical Cavity of same height and same diameter is hollowed out from a cylinder of height h and base radius r, then the volume of the cone is equal to $\frac{1}{3}$ of the volume of cylinder

a)

Both (A) and (R) are true and (R) is the correct explanation of (A)

b)

Both (A) and (R) are true and (R) is not the correct explanation of (A)

c)

(A) is true but (R) is false

d)

(A) is false but (R) is true

32.

Assertion (A): Combining a right circular cone with a hemisphere results in a shape with a larger TSA than each individual shape.

Reason (R): The addition of the CSA of the cone to the CSA of hemisphere increases the TSA of the combined shape

a)

Both (A) and (R) are true and (R) is the correct explanation of (A)

b)

Both (A) and (R) are true and (R) is not the correct explanation of (A)

c)

(A) is true but (R) is false

d)

(A) is false but (R) is true

33.

A mason constructs a wall of dimensions (270 cm x 300cm x 350cm) with bricks, each of size (22.5cm x 11.25cm x 8.75cm) and it is assumed that $\frac{1}{8}$ space is covered by the mortar. Number of bricks used to construct the wall is

a)

11000

b)

11100

c)

11200

d)

11300

34.

If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is

a)

1:2

b)

2:1

c)

1:4

d)

4:1

35.

In a shower, 5cm of rain falls. The volume of the water that falls on 2 hectares of ground is

a)

$100\ m^3$

b)

$10\ m^3$

c)

$1000\ m^3$

d)

$10000\ m^3$

36.

In a right circular cone, the cross section made by a plane parallel to the base is a

a)

Sphere

b)

Hemisphere

c)

Circle

d)

a semicircle

37.

Assertion(A): If the volumes of two spheres are in the ratio 64:27, then the ratio of their surface areas is 4:3

Reason (R): If the surface areas of two spheres are in the ratio 16:9, then the ratio of their volumes is 64:27

a)

Both (A) and (R) are true and Reason (R)is the correct explanation of Assertion (A)

b)

Both (A) and (R) are true and Reason (R)is not the correct explanation of Assertion (A)

c)

Assertion (A) is true but Reason (R)is false

d)

Assertion (A) is false but Reason (R)is true

38.

Assertion(A): The Volume of a right circular cylinder of base radius 7cm and height 10cm is $1540\ cm^{3\ }$

Reason(R): According to assertion, the curved surface area of cylinder is $440cm^2$

a)

Both (A) and (R) are true and Reason (R)is the correct explanation of Assertion (A)

b)

Both (A) and (R) are true and Reason (R)is not the correct explanation of Assertion (A)

c)

Assertion (A) is true but Reason (R)is false

d)

Assertion (A) is false but Reason (R)is true

39.

Assertion(A): If the height of the cone is 10cm and the radius of the base is 7cm, then the volume of the cone is $513.3cm^2$

Reason(R): According to assertion, if $\sqrt[]{149}=12.2$ , then curved surface area of a cone is $268.4cm^2$

a)

Both (A) and (R) are true and Reason (R)is the correct explanation of Assertion (A)

b)

Both (A) and (R) are true and Reason (R)is not the correct explanation of Assertion (A)

c)

Assertion (A) is true but Reason (R)is false

d)

Assertion (A) is false but Reason (R)is true

40.

The radius of a sphere (in cm) whose volume is $12\pi\ cm^3$ , is

a)

3

b)

$3\ \sqrt[]{3}$

c)

$3^{\frac{2}{3}}$

d)

$3^{\frac{1}{3}}$

Area Related to Circles & Surface area and Volumes

Total questions: 40

Worksheet time: 40mins

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