This set of Aptitude Questions and Answers (MCQs) focuses on “Cone – Set 2”.

1. Which of the following is the correct formula for the slant height of a cone?

a) √(4h^{2} + r^{2})

b) √(2h^{2} + 2r^{2})

c) √(h^{2} + 4r^{2})

d) √(h^{2} + r^{2})

View Answer

Explanation: Let the radius of the cone be r and height be h.

Then, slant height = √(h

^{2}+ r

^{2}).

2. What will be the curved surface area of a cone of radius 7 cm and slant height 10 cm?

a) 220 cm^{2}

b) 260 cm^{2}

c) 280 cm^{2}

d) 180 cm^{2}

View Answer

Explanation: Given,

r = 7 cm, l = 10 cm

Curved surface area = πrl

= (22 / 7) * (7) * (10)

= 220 cm

^{2}

3. What is the total surface area (in sq. cm) of a cone of radius 3 cm and slant height of 4 cm?

a) 62

b) 66

c) 76

d) 73

View Answer

Explanation: Given,

r = 3 cm, l = 4 cm

Total surface area = πr (r + l)

= (22 / 7) * 3 * (3 + 4)

= 66 cm

^{2}

4. What will be the slant height of a cone of radius 3 cm and height of 4 cm?

a) 5 cm

b) 6 cm

c) 6.5 cm

d) 5.5 cm

View Answer

Explanation: Given,

r = 3 cm, h = 4 cm

l = √(h

^{2}+ r

^{2})

l = (3

^{2}+ 4

^{2})

^{1/2}

l = (9 + 16)

^{1/2}

l = (25)

^{1/2}

l = 5 cm

5. What will be the volume (in cubic cm) of a cone of radius of 6 cm and slant height of 14 cm?

a) 338

b) 420

c) 528

d) 510

View Answer

Explanation: Given,

r = 8 cm, l = 14 cm

Volume = 1 / 3 πr

^{2}l

= 1 / 3 * (22 / 7) * (6)

^{2}* (14)

= 1 / 3 * (22 / 7) * 36 * 14

= 528 cm

^{3}

6. What will be the slant height of a cone of radius 6 cm and curved surface area of 300 cm^{2}?

a) 24.6 cm

b) 18.6 cm

c) 27.5 cm

d) 15.9 cm

View Answer

Explanation: Given,

Curved surface area = 300 cm

^{2}, r = 6 cm.

Curved surface area = πrl

Let the slant height = l

➩ 300 = (22 / 7) * 6 * l

➩ 300 * 7 / (22 * 6) = l

➩ 15.9 cm = l

7. What will be the diameter of a cone having radius equal to the slant height of the cone with curved surface area as 4200 cm^{2}?

a) 73 cm

b) 68 cm

c) 77 cm

d) 65 cm

View Answer

Explanation: Given,

Curved surface area = 4200 cm

^{2}

Let the radius = z, then slant height will also be = z.

Curved surface area = πrl

➩ 4200 = (22 / 7) * z * z

➩ 4200 * 7 / 22 = z

^{2}

➩ 1336.36 = z

^{2}

➩ z = 36.5 cm

Thus, diameter = 2 * 36.5 cm

= 73 cm

8. A cone is having radius as 7 cm and slant height as 15 cm. What will be its volume when it is two – third filled with water?

a) 549.33 cm^{3}

b) 526.66 cm^{3}

c) 513.33 cm^{3}

d) 498.66 cm^{3}

View Answer

Explanation: Given,

Two – third filled cone, r = 7 cm, l = 15 cm

Volume = (2 / 3) * 1 / 3 πr

^{2}l

= 2 / 3 * 1 / 3 * 22 / 7 * 72 * 15

= 2 / 3 * 1 / 3 * 22 / 7 * 49 * 15

= 513.33 cm

^{3}

9. If the radius of a cone is increased to three times its initial value, then how many times will the curved surface area become?

a) 9 times

b) 3 times

c) 12 times

d) 6 times

View Answer

Explanation: Let the original radius = r

Original curved surface area = πrl

New radius = 3r

New curved surface area = π(3r) * l

Thus, the new curved surface area is 3 times the original value.

10. The slant height of a cone is increased to two times of its initial value, then the new volume of this cone will become how many times of the initial volume?

a) Two times

b) Three times

c) Four times

d) Eight times

View Answer

Explanation: Let the initial slant height = l

Initial volume = 1 / 3 πr

^{2}l

New slant height = 2l

New volume = 1 / 3 πr

^{2}(2l)

Thus, the new volume is two times the original volume.

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