Choose the correct alternative answer for each of the following questions.

(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 = r²
Given ratio of circumference and area = 2:7
2r/r² = 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 cm² (B) 550 cm² (C) 330 cm² (D) 110 cm²

Solution:
Given height , h = 24cm
Radius , r = 7cm
Slant height l = √(h²+r²)
= √(24²+7²)
= √(576+49)
=√625
= 25cm
Curved surface area of a cone = rl
= 22/7)×7×25
= 22×25
=550cm²
Hence option B is the answer.

(5) The curved surface area of a cylinder is 440 cm² 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 = 440cm²
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)r²h = r²H
h = 5×3 = 15cm
Hence option A is the answer.

(7) Find the volume of a cube of side 0.01 cm.
(A) 1 cm³ (B) 0.001 cm³ (C) 0.0001 cm³ (D) 0.000001 cm³

Solution:
Volume of a cube ,V= a³
Given side , a = 0.01
V = 0.01³ = 0.000001cm³
Hence option D is the answer.

(8) Find the side of a cube of volume 1 m³ .
(A) 1 cm (B) 10 cm (C) 100 cm (D)1000 cm

Solution:
Given volume , V = 1m³
Volume of cube of side a = a³
a³ = 1m³
a =1m = 100cm
Hence option C is the answer.