Question
Two cylinders $A$ and $B$ are formed by folding a rectangular sheet of dimensions $20\ cm × 10\ cm$ along its length and also along its breadth respectively. Then volume of $A$ is ________ of volume of $B.$
✓
Answer
We have a rectangular sheet of dimensions $20\ cm × 10\ cm.$
If we fold it along its length, which is $20\ cm,$ then the resultant figure is a cylinder with height, $h = 10\ cm$ and base circumference, $2\pi\text{r}=20\text{cm}$
$\Rightarrow\text{r}=\frac{20}{2\pi}=\frac{10}{\pi}\text{cm}$
$\therefore$ The volume of the cylinder, so formed $=\pi\text{r}^2\text{h}$
$=\pi\times\frac{10}{\pi}\times\frac{10}{\pi}\times10$
$=\frac{1000}{\pi}\text{cm}^3$
$=\text{V}_1\text{(say)}$
Again, if we fold the rectangular sheet along its breadth, which is $10\ cm,$ the figure so obtained is a cylinder with height, $h = 20\ cm$ and the base circumference $2\pi\text{r}=10\text{cm}$
$\Rightarrow\text{r}=\frac{10}{2\pi}=\frac{5}{\pi}\text{cm}$
$\therefore$ Volume of the cylinder $=\pi\text{r}^2\text{h}=\pi\times\frac{5}{\pi}\times\frac{5}{\pi}\times20$
$=\frac{500}{\pi}\text{cm}^3$ = $V_2$ (say)
i.e. $V_2 = 2V_1$
From Eqs. $(i)$ and $(ii),$ we see that the volume of $A$ is twice the volume of $B.$
If we fold it along its length, which is $20\ cm,$ then the resultant figure is a cylinder with height, $h = 10\ cm$ and base circumference, $2\pi\text{r}=20\text{cm}$
$\Rightarrow\text{r}=\frac{20}{2\pi}=\frac{10}{\pi}\text{cm}$
$\therefore$ The volume of the cylinder, so formed $=\pi\text{r}^2\text{h}$
$=\pi\times\frac{10}{\pi}\times\frac{10}{\pi}\times10$
$=\frac{1000}{\pi}\text{cm}^3$
$=\text{V}_1\text{(say)}$
Again, if we fold the rectangular sheet along its breadth, which is $10\ cm,$ the figure so obtained is a cylinder with height, $h = 20\ cm$ and the base circumference $2\pi\text{r}=10\text{cm}$
$\Rightarrow\text{r}=\frac{10}{2\pi}=\frac{5}{\pi}\text{cm}$
$\therefore$ Volume of the cylinder $=\pi\text{r}^2\text{h}=\pi\times\frac{5}{\pi}\times\frac{5}{\pi}\times20$
$=\frac{500}{\pi}\text{cm}^3$ = $V_2$ (say)
i.e. $V_2 = 2V_1$
From Eqs. $(i)$ and $(ii),$ we see that the volume of $A$ is twice the volume of $B.$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
$38 x^3 y^2 z \div 19 x y^2$ is equal to _________.
→Write true $(T)$ or false $(F)$ for the following statements.
The product of two square numbers is a square number.
→The product of two square numbers is a square number.
$a^2- b^2$ is equal to:
→Name of the following parallelogram.
All the sides are equal and one angle is $90^\circ .$
→All the sides are equal and one angle is $90^\circ .$
Count the number of cubes in the given shapes.
Two cuboids with equal volumes will always have equal surface areas.
What could be the possible 'one's' digits of the square root of $99856.$
→Find the cube of the following numbers:$12$
→$67^2-37^2=(67-37) ×$ ________ $=$ _________.
→If amount on the principal of $Rs. 6,000$ is written as $6000 \Big[1+\frac{5}{100}\Big]^3$and compound interest payable half yearly, then rate of interest p.a. is _______ and time in years is _______.
→