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Multiple choice maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

The ratio between the radius of the base and the height of a cylinder is $2:3$. If its volume is $12936$ cu. cm, the total  surface area of the cylinder is :

  1. $2587.2 c{m^2}$
  2. $3080 c{m^2}$
  3. $25872 c{m^2}$
  4. $38808 c{m^2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
We have $\dfrac{r}{h}=\dfrac{2}{3}\Rightarrow\,h=\dfrac{3r}{2}$

Volume of a cylinder$=\pi{r}^{2}h$

$\Rightarrow\,12936=\dfrac{22}{7}\times{r}^{2}\times \dfrac{3r}{2}$

$\Rightarrow\,12936=\dfrac{11\times 3}{7}{r}^{3}$

$\Rightarrow\,{r}^{3}=\dfrac{12936\times 7}{33}=2744$

$\Rightarrow\,r=\sqrt[3]{2744}=14\ cm$

We have $h=\dfrac{3r}{2}=\dfrac{3\times 14}{2}=21\ cm$

Total Surface area$=2\pi\,r\left(r+h\right)=2\times\dfrac{22}{7}\times 14\left(14+21\right)=2\times\dfrac{22}{7}\times 14\times 35=140\times 22=3080\ sq.cm$
Multiple choice maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

A cylinder and cone of equal base radius and equal height are given. Which of the following statement is true/

  1. Volume of cylinder and cone are equal

  2. Volume of cylinder is one-third of volume of cone

  3. Volume of cone is half of the volume of cylinder

  4. Volume of cone is one-third of volume of cylinder
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The volume of a cylinder is given by V_cyl = pi r^2 h, while the volume of a cone with the same base radius and height is V_cone = (1/3) pi r^2 h. Therefore, the volume of the cone is exactly one-third of the volume of the cylinder.

Multiple choice maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

A cylindrical pipe is made from a metal sheet of length 88 cm and breadth 20 cm. What is the volume of this pipe?

  1. $2800$ ${ cm }^{ 3 }$
  2. $12320$ ${ cm }^{ 3 }$
  3. $13202$ ${ cm }^{ 3 }$
  4. $13220$ ${ cm }^{ 3 }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We have,

Length $l=88\,cm.$

Breadth$b=20\,cm.$

Volume $=?$

Volume of cylindrical pipe $=\pi {{r}^{2}}h$

We know that,

$ circumfrance=Breadth=2\pi r $

$ 2\pi r=20 $

$ \pi r=10 $

$ r=\dfrac{10}{\pi } $

$ r=\dfrac{10}{\dfrac{22}{7}} $

$ r=\dfrac{70}{22} $

$ r=\dfrac{35}{11}\,\,cm. $

Then,

Volume of cylindrical pipe $V=\pi {{r}^{2}}h$

$ V=\dfrac{22}{7}\times \dfrac{35}{11}\times \dfrac{35}{11}\times 88 $

$ V=2\times 5\times 35\times 8 $

$ V=80\times 35 $

$ V=2800\,c{{m}^{3}} $

Hence, this is the answer.

Multiple choice maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

If sum of radius and height of a cylinder is 6, then its maximum volume is 

  1. $32\pi$
  2. $16\pi$
  3. $8\pi$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume V = pi * r^2 * h. Given r + h = 6, then h = 6 - r. V(r) = pi * r^2 * (6 - r) = pi * (6r^2 - r^3). To maximize, V'(r) = pi * (12r - 3r^2) = 0. So 3r(4 - r) = 0, r = 4. Then h = 2. Max Volume = pi * 4^2 * 2 = 32 * pi.

Multiple choice maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

Mark the correct alternative of the following.
Two cylindrical jars have their diameters in the ratio $3:1$, but height $1:3$. Then the ratio of their volumes is?

  1. $1:4$
  2. $1:3$
  3. $3:1$
  4. $2:5$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let $V _1$ and $V _2$ be the volume of the two cylinders with radius $r _1$ and height $h _1$, and radius $r _2$ and height $h _2.$

$\dfrac{2r _1}{2r _2}=\dfrac{3}{1}$ and $\dfrac{h _1}{h _2}=\dfrac{1}{3}$             [ Given ]
So,
$V _1=\pi r _1^2h _1$           ----- ( 1 )
Now,
$V _2=\pi r _2^2h _2$            ---- ( 2 )
From equation ( 1 ) and ( 2 ), we get
$\dfrac{V _1}{V _2}=\left(\dfrac{r _1}{r _2}\right)^2\left(\dfrac{h _1}{h _2}\right)$

$\Rightarrow$  $\dfrac{V _1}{V _2}=\left(\dfrac{2r _1}{2r _2}\right)^2\left(\dfrac{h _1}{h _2}\right)$

$\Rightarrow$  $\dfrac{V _1}{V _2}=(3)^2\left(\dfrac{1}{3}\right)$

$\Rightarrow$  $\dfrac{V _1}{V _2}=\dfrac{3}{1}$

Multiple choice maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

Mark the correct alternative of the following.
In a cylinder, if radius is doubled and height is halved, curved surface area will be?

  1. Halved

  2. Doubled

  3. Same

  4. Four times
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the radius of cylinder be $r$ and height be $h.$

So, the original curved surface area $=2\pi rh$
When, radius is doubled and height is halved,
New curved surface area $=2\pi \times 2r\times \dfrac{h}{2}$

                                           $=2\pi r h$
$\therefore$  New curved surface area $=$ Original surface area.
$\therefore$  There is no change in the curved surface area of the cylinder