Tag: surface area of a cone

Questions Related to surface area of a cone

The base radii of a cone and a cylinder are equal. If their curved surface areas are also equal, then the ratio of the slant height of the cone to the height of the cylinder is

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

  1. $2 : 1$

  2. $1 : 2$

  3. $1 : 3$

  4. $3 : 1$

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Correct Option: A
Explanation:
Let the radius of the cone and cylinder be $r$.
The base radii of cone and cylinder are equal.
Given curved surface areas are equal,
$\therefore (\pi)rl = 2(\pi)rh$
$\therefore \dfrac {l}{h}=2$
Hence, option A is correct.

The height of a conical tent at the center is $5 m$, the distance of any point on its circular base from the top of the tent is $13 m$. The area of the slant surface is 

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

  1. $144 \pi sq. m$

  2. $130 \pi sq. m$

  3. $156 \pi sq. m$

  4. $169 \pi sq. m$

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Correct Option: C
Explanation:

Given Height $h=5$ and Slant height $l=13$


$\Rightarrow r^{2}=l^{2}-h^{2}=13^{2}-5^{2}$

$\Rightarrow r=12 $

Area of slant surface $=\pi rl$

                                    $=\pi ×12×13$

$\Rightarrow $area of slant surface $=156\pi$ sq.m

If the base area of a cone is 616 sq.cm., its height is
48cm, then its slant height is

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

  1. 25

  2. 50

  3. 18

  4. 8

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Correct Option: B

If the base radius and slant height of a right circular cone are $10 \,cm$ and $3.5 \,cm$ respectively, then its total surface area is

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

  1. $424.159 cm^2$

  2. $434.159 cm^2$

  3. $414.159 cm^2$

  4. None of these

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Correct Option: A
Explanation:

Given the radius of the base of a right circular cone $(r)=10$ cm, and its slant height $(l)=3.5$ cm.


Then its total surface area $=\pi r^2+\pi rl=\dfrac{22}{7}\times 100+\dfrac{22}{7}\times 10\times 3.5=314.159+110=424.159$ cm$^2$.

If the radius of the base of a right circular cone is $2 \,cm$ and its slant height is $3.5 \,cm$, then its curved surface area is

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

  1. $44 \,cm^2$

  2. $77 \,cm^2$

  3. $22 \,cm^2$

  4. $154 \,cm^2$

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Correct Option: C
Explanation:

Given the radius of the base of a right circular cone $(r)=2$ cm, and its slant height $(l)=3.5$ cm.

Then its curved surface area $=\pi rl=\dfrac{22}{7}\times 2\times 3.5=22$ cm$^2$.

Diameter of the base of a cone is $10.5$cm and its slant height is $10$cm. Find its curved surface area.

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

  1. $104.85cm^2$

  2. $164.85cm^2$

  3. $100.75cm^2$

  4. None of these

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Correct Option: B
Explanation:
diameter of box $=10.5\ cm$
radius $=\dfrac{10.5}{2}=5.25\ cm$
height $=l=10\ cm$
curved surface area $=(52.5 \pi)\ cm^{2}$
$\therefore$ Curved surface area of the given cone is $164.85\ cm^{2}$

If a right circular cone having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (in ${ cm }^{ 2 }$ ) of this cone is

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

  1. $8\sqrt { 3\pi } $

  2. $6\sqrt { 2\pi } $

  3. $6\sqrt { 3\pi } $

  4. $8\sqrt { 2\pi } $

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Correct Option: A

The $T.S.A$ of a cone whose $d=14\ cm$, $h=24\ cm$

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

  1. $504\ cm^{2}$

  2. $3696\ cm^{2}$

  3. $704\ cm^{2}$

  4. $528\ cm^{2}$

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Correct Option: A

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

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

  1. $440\ \text{cm}^2$

  2. $550\ \text{cm}^2$

  3. $330\ \text{cm}^2$

  4. $110\ \text{cm}^2$

Show answer
Correct Option: B
Explanation:
Radius $r = 7 cm$

Height $h = 24 cm$

To find slant height $l$

$l _{2}^{2}=r^{2}+h^{2}$

$l^{2}=7^{2}+24^{2}$

$l^{2}=625$

$l=25 cm $

Curved surface area of cone is $\pi rl$

                               $=\dfrac{22}{7}\times 7\times 25$

                               $= 22\times 25$

                               $=550 cm ^{2}$

Curved surface area of cone is $550cm^{2}$

Mark the correct alternative of the following.
A right circular cylinder and a right circular cone have the same radius and the same volume. The ratio of the height of the cylinder to that of the cone is?

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

  1. $3:5$

  2. $2:5$

  3. $3:1$

  4. $1:3$

Show answer
Correct Option: D
Explanation:

It is given that, the volumes of both cylinder and cone are the same.

So, let volume of the cylinder and cone be $V.$
It is also given that, their base radii are the same.
So, let radius of the cylinder $=$ Radius of the cone $=r$
Let the height of the cylinder and the cone be $h _1$ and $h _2$ respectively.
Volume of cone $=\dfrac{1}{3}\pi r^2 h _2$
Volume of cylinder $=\pi r^2 h _1$
We know both volumes are same.
$\therefore$  $\dfrac{1}{3}\pi r^2 h _2=\pi r^2 h _1$

$\Rightarrow$  $\dfrac{h _1}{h _2}=\dfrac{\pi r^2}{3\pi r^2}$

$\therefore$  $\dfrac{h _1}{h _2}=\dfrac{1}{3}$