Tag: solids

Questions Related to solids

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. $169 \pi sq. m$

Show answer
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

Show answer
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. $154 \,cm^2$

Show answer
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

Show answer
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 } $

Show answer
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. $528\ cm^{2}$

Show answer
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.
$\therefore$  $\dfrac{1}{3}\pi r^2 h _2=\pi r^2 h _1$

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

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

Mark the correct alternative of the following.
If the base radius and the height of a right circular cone are increased by $20\%$, then the percentage increase in volume is approximately.

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

  1. $60$

  2. $68$

  3. $73$

  4. $78$

Show answer
Correct Option: C
Explanation:
Let original radius of base and height are $R$ and $H$ respectively.
Original height $=H$

New radius $=\dfrac{120}{100}R=\dfrac{6}{5}R$

And new height $=\dfrac{6}{5}H$

Original volume of cone $V _1=\dfrac{1}{3}\pi R^2 H$

New volume of cone $V _2=\dfrac{1}{3}\pi \left(\dfrac{6}{5}R\right)^2\times \dfrac{6}{5}H$

                                          $=\dfrac{216}{125}V _1$

Now, increased in volume $=\dfrac{216}{125}V _1-V _1=\dfrac{91}{125}V _1$

$\therefore$  Percentage increased in volume $=\left(\dfrac{91}{125}V _1\times\dfrac{1}{V _1}\right)\times 100\%$

                                                              $=72.81\%\approx 73\%$