Tag: hollow cylinder

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

If volume of sphere is $850$ $m^{3}$ then its radius and surface area are

  1. $6m$, $450$ $m^{2}$
  2. $5m$, $560$ $m^{2}$
  3. $2m$, $780$ $m^{2}$
  4. $5.88m$, $434$ $m^{2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Volume of Sphere $=850m^3=\cfrac{4}{3}\pi r^3 \Rightarrow r^3=\cfrac{850\times 3\times 7}{4\times 22}=202.84 \\ \Rightarrow r=\sqrt[3]{202.84}=5.88m$
Surface area $=4\pi r^2=4\times \cfrac{22}{7}\times 5.88\times 5.88 \approx 434m^2$
Multiple choice maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

A test-tube consists of a hollow cylindrical tube joined to a hemi-spherical bown of the same internal radius. The whole tube holds $350$ cc of water and in the cylindrical portion falls $1$ cm if $19.64$ cc of water is removed. Find the length of the cylindrical portion of the tube. (Take $\pi =$ $22/7$)

  1. $12.15$ cm
  2. $16.15 $ cm
  3. $24.15 $ cm

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

Let r cm. be the radius of the hemisphere and h cm be the length of the cylindrical portion.
Volume of water removed $\pi r^2 (1) = 19.64cc$
$\Rightarrow r^2 = 19.64 \times \displaystyle \frac{7}{22}  \Rightarrow r = 2.5 cm$
Volume of the whole tube $= \pi r^2 h + \displaystyle \frac{2}{h} \pi r^3 = 350 c.c.$
$\Rightarrow \pi r^2 \displaystyle \left ( h + \frac{2}{3} r \right ) = 350$
$\Rightarrow \displaystyle \frac{22}{7} \times 2.5^2 \times \left ( h + \frac{2}{3} \times 2.5 \right ) = 350$
$\displaystyle \frac{22}{7} \times 6.25 \times (h+ 1.67) = 350 $
$ \Rightarrow \displaystyle 350 \times \frac{7}{22} \times 6. 25 - 1.67 cm    \Rightarrow h = 16.15 cm$

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

The height of a hollow cylinder is $14cm$ if external diameter is $16cm$ and total curved surface area of the hollow cylinder is $1320sq.cm$, then its internal diameter is

  1. $14cm$
  2. $16cm$
  3. $7cm$
  4. $8cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given     

external radius $r _2=8$, height of cylinder $h=14$
 we have,


$2\pi h(r _{1}+r _{2})=1320$

$ \implies8+r _1=\displaystyle \frac{1320\times7}{2\times22\times14}$

$\implies r _1=7cm$

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$=2\pi\,r\left(r+h\right)=2\times\dfrac{22}{7}\times 14\left(14+21\right)=2\times\dfrac{22}{7}\times 14\times 35=140\times 22=3080\ sq.cm$