Tag: surface area of a cone

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Multiple choice maths solids surface area of a cone surface area of cone the surface area of a cone

A cone and a cylinder have the same base area. They also have the same curved surface area. If the height of the cylinder is $3$ m, then the slant height of the cone (in m) is

  1. $3$
  2. $4$
  3. $6$
  4. $7$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given the radius of cylinder and cone are the same because there base areas are same.
Curved surface of cylinder $=$ curved surface area of the cone
$\therefore 2 \pi r h = \pi r l$
$\therefore l = 2h $
Given, height of cylinder $= 3$ cm
Therefore, slant height of cone $= 6$ cm

Multiple choice maths solids surface area of a cone surface area of cone the surface area of a cone

The curved surface area of a right circular cone with height $24$ cm and radius $7$ cm is

  1. $500 cm^2$
  2. $550 cm^2$
  3. $607 cm^2$
  4. $650 cm^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given,
Radius of cone $= 7$ cm
Height of cone $= 24$ cm
Curved surface area = $\pi r \sqrt{(r^2 + l^2)}$
= $\pi \times 7 (\sqrt{(7^2 + (24)^2)}$
= $\pi \times 70\times 25$
= $550 cm^2$

Multiple choice maths solids surface area of a cone surface area of cone the surface area of a cone

Consider two cones, the curved surface area of one being twice that of the other and the slant height of the later being twice that of the former. The ratio of the radius of the later cone to that of the former is

  1. $1 : 4$
  2. $1 : 2$
  3. $2 : 1$
  4. $4 : 1$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the curved surface areas of two cones be $C _1$ and $C _2$

And their slant heights be $l _1$ and $l _2$
Given, $C _1=2C _2$
$l _2=2l _1$

$\therefore \pi r _1l _1=2\pi r _2.2l _1$
$\therefore r _1=4r _2$

Multiple choice maths solids surface area of a cone surface area of cone the surface area of a cone

The curved surface area of a right cone is $\displaystyle 286 m^{2}$ and its the slant height is 13 m, then volume is

  1. $\displaystyle 821.389m^{3}$
  2. $\displaystyle 852.258m^{3}$
  3. $\displaystyle 364.369m^{3}$
  4. $\displaystyle 281.164m^{3}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Curved surface area of a cone $= \pi rl$  where r is
the radius of the cone and l is the slant height.
Hence, CSA of this cone, $ = \frac {22}{7} \times r \times 13 = 286 $
$ => r = 7  m $

For a cone, l $ = \sqrt { { h }^{ 2 }+  {r}^{ 2 } } $ where lis the slant height.

Hence, $ 13 = \sqrt { { h }^{ 2 }+  {7}^{ 2 } } $ 

$ 169 = { h }^{ 2 } + 49 $

$ { h }^{ 2 } = 120 $

$ h = 2 \sqrt {30}  m $

Hence, volume of this cone $ = \frac { 1 }{ 3 } \times \frac { 22 }{ 7 } \times { 7 }^{ 2 }\times 2 \sqrt {30} = \frac {154}{3} \sqrt {30} { m }^{ 3 } $


Multiple choice maths solids surface area of a cone surface area of cone the surface area of a cone

The cost of the canvas required to make a conical tent of base radius $8$ m at the rate of Rs. $40$ per $\displaystyle m^{2}$ is Rs. $10,048$. Find the height of the tent .$\displaystyle \left ( Take\  \pi =3.14 \right )$ 

  1. $6$ m
  2. $7$ m
  3. $8$ m
  4. $10$ m
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To find the amount of canvas required to make a conical tent, we need to calculate the lateral surface area of the tent.
Lateral surface area of a cone of radius $ r $, height $ h = \pi r\sqrt{{h}^{2} + {r}^{2}} $
As the total cost to make the tent is Rs $10048 $ at the rate of Rs $ 40 $ per sq m, total area LSA $ = \dfrac {10048}{40} = 251.2 $ sq m 

So, $ \pi r \times \sqrt{{h}^{2} + {r}^{2}} = 251.2 $
$ \Rightarrow  3.14 \times 8 \times \sqrt{{h}^{2} + {8}^{2}} = 251.2 $
$ \Rightarrow  \sqrt{{h}^{2} + {8}^{2}} = 10 $
$ \Rightarrow  {h}^{2} + 64 = 100 $
$ \Rightarrow  {h}^{2}  = 36 $
$ \Rightarrow  h = 6 $ m