**(1) The ratio of circumference and area of a circle is 2:7. Find its circumference.****(A) 14 (B) 7/ (C) 7 (D) 14/**

**Solution:**

Circumference of circle = 2r

Area of circle = r^{2}

Given ratio of circumference and area = 2:7

2r/r^{2} = 2/7

2/r = 2/7

r = 7cm

Circumference = 2r = 2×7 = 14.

Hence option A is the answer.

**(2) If measure of an arc of a circle is 160° and its length is 44 cm, find the circumference of the circle.****(A) 66 cm (B) 44 cm (C) 160 cm (D) 99 cm**

**Solution:**

Given measure of arc = 160˚

Length of arc = 44cm

Length of arc = (/360)2r

44 = (160/360)×2r

2r = 44×360/160 = 99

Circumference = 2r

Hence circumference is 99cm

So option D is the answer.

**(3) Find the perimeter of a sector of a circle if its measure is 90 ° and radius is 7 cm.****(A) 44 cm (B) 25 cm (C) 36 cm (D) 56 cm**

**Solution:**

Given radius , r = 7cm

= 90˚

Perimeter of a sector = 2r + length of arc

= 2r + (/360)2r

= 2×7 + (90/360)×2×(22/7)×7

= 14+11

= 25cm

Hence option B is the answer.

**(4) Find the curved surface area of a cone of radius 7 cm and height 24 cm.****(A) 440 cm ^{2} (B) 550 cm^{2} (C) 330 cm^{2} (D) 110 cm^{2}**

**Solution:**

Given height , h = 24cm

Radius , r = 7cm

Slant height *l* = √(h^{2}+r^{2})

= √(24^{2}+7^{2})

= √(576+49)

=√625

= 25cm

Curved surface area of a cone = r*l*

= 22/7)×7×25

= 22×25

=550cm^{2}

Hence option B is the answer.

**(5) The curved surface area of a cylinder is 440 cm ^{2} and its radius is 5 cm. Find its height.**

**(A) 44 / cm (B) 22 cm (C) 44 cm (D) 22/ cm**

**Solution:**

Given radius , r = 5cm

Curved surface area = 440cm^{2}

Curved surface area = 2rh

440 = 2rh

h = 440/2r

= 440/(2×5)

= 440/10

= 44

Hence option C is the answer.

**(6) A cone was melted and cast into a cylinder of the same radius as that of the base of the cone. If the height of the cylinder is 5 cm, find the height of the cone.****(A) 15 cm (B) 10 cm (C) 18 cm (D) 5 cm**

**Solution:**

Given radius of both cone and cylinder are equal.

Height of cylinder,H = 5cm

Let height of cone be h.

Since cone is melted and cast into a cylinder, volume of cone is equal to volume of cylinder.

(1/3)r^{2}h = r^{2}H

h = 5×3 = 15cm

Hence option A is the answer.

**(7) Find the volume of a cube of side 0.01 cm.****(A) 1 cm ^{3} (B) 0.001 cm^{3} (C) 0.0001 cm^{3} (D) 0.000001 cm^{3}**

**Solution:**

Volume of a cube ,V= a^{3}

Given side , a = 0.01

V = 0.01^{3} = 0.000001cm^{3}

Hence option D is the answer.

**(8) Find the side of a cube of volume 1 m ^{3} .**

**(A) 1 cm (B) 10 cm (C) 100 cm (D)1000 cm**

**Solution:**

Given volume , V = 1m^{3}

Volume of cube of side a = a^{3}

a^{3} = 1m^{3}

a =1m = 100cm

Hence option C is the answer.