Tag: surface area of a cone

Quizzes (0) Questions (85)

Questions Related to surface area of a cone

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

  1. $2 : 1$
  2. $1 : 2$
  3. $1 : 3$
  4. $3 : 1$
Reveal answer Fill a bubble to check yourself
A Correct answer
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.
Multiple choice maths solids surface area of a cone surface area of cone the surface area of a cone

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 

  1. $144 \pi sq. m$
  2. $130 \pi sq. m$
  3. $156 \pi sq. m$
  4. $169 \pi sq. m$
Reveal answer Fill a bubble to check yourself
C Correct answer
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

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

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

  1. $424.159 cm^2$
  2. $434.159 cm^2$
  3. $414.159 cm^2$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
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$^2$.

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

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

  1. $44 \,cm^2$
  2. $77 \,cm^2$
  3. $22 \,cm^2$
  4. $154 \,cm^2$
Reveal answer Fill a bubble to check yourself
C Correct answer
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$^2$.

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

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

  1. $104.85cm^2$
  2. $164.85cm^2$
  3. $100.75cm^2$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $164.85\ cm^{2}$
Multiple choice maths solids surface area of a cone surface area of cone the surface area of a cone

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

  1. $8\sqrt { 3\pi } $
  2. $6\sqrt { 2\pi } $
  3. $6\sqrt { 3\pi } $
  4. $8\sqrt { 2\pi } $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a cone of maximum volume inscribed in a sphere of radius R, the height h = 4R/3 = 4 cm and radius r = sqrt(8/9) * R = sqrt(8) cm. The slant height l = sqrt(r^2 + h^2) = sqrt(8/9 * 9 + 16) = sqrt(8 + 16) = sqrt(24) = 2*sqrt(6). Curved surface area = pi * r * l = pi * sqrt(8) * 2*sqrt(6) = pi * 2*sqrt(2) * 2*sqrt(6) = 8*sqrt(3)*pi. The provided answer matches this form.

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

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

  1. $504\ cm^{2}$
  2. $3696\ cm^{2}$
  3. $704\ cm^{2}$
  4. $528\ cm^{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total surface area of a cone is given by pi * r * (l + r). Given diameter d = 14 cm, radius r = 7 cm, height h = 24 cm, the slant height l = sqrt(7^2 + 24^2) = 25 cm. Thus TSA = (22 / 7) * 7 * (25 + 7) = 22 * 32 = 704 cm^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 cone of radius $7$ cm and height $24$ cm is

  1. $440\ \text{cm}^2$
  2. $550\ \text{cm}^2$
  3. $330\ \text{cm}^2$
  4. $110\ \text{cm}^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $550cm^{2}$
Multiple choice maths solids surface area of a cone surface area of cone the surface area of a cone

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?

  1. $3:5$
  2. $2:5$
  3. $3:1$
  4. $1:3$
Reveal answer Fill a bubble to check yourself
D Correct answer
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.
$\therefore$  $\dfrac{1}{3}\pi r^2 h _2=\pi r^2 h _1$

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

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