 |
$\begin{align}(i)\text{Volume of a cylinder}&=\pi r^2\times h\\[5pt]
&=400\times 10\\[5pt]
&=\underline{\underline{4000cm^3}}\\
\end{align}$ | $\begin{align}(ii)\text{Volume of a cylinder}&=\pi r^2\times h\\[5pt]
&=\frac{22}{7}\times 7\times 7\times 15\\[5pt]
&=22\times 7\times 15\\[5pt]
&=\underline{\underline{2310cm^3}}\\
\end{align}$ |
$\begin{align}(iii)\text{Volume of a cylinder}&=\pi r^2\times h\\[5pt]
&=\frac{22}{7}\times \frac{21}{2}\times \frac{21}{2}\times 20\\[5pt]
&=11\times 3\times 21\times 10\\[5pt]
&=\underline{\underline{6930cm^3}}\\
\end{align}$
|
|
 |
$\begin{align}\text{Area of the cross section}&=\pi r^2\times h\\[5pt]
&=\frac{22}{7}\times 7\times 7\\[5pt]
&=22\times 7\\[5pt]
&=\underline{\underline{154cm^3}}\\
\end{align}$
$\begin{align}(a)\text{Volume of a cylinder}&=\pi r^2\times h\\[5pt]
&=154\times 8\\[5pt]
&=\underline{\underline{1232cm^3}}\\
\end{align}$ | $\begin{align}(b)\text{Volume of a cylinder}&=\pi r^2\times h\\[5pt]
&=154\times 16\\[5pt]
&=\underline{\underline{2464cm^3}}\\
\end{align}$
$\begin{align}(c)\text{Volume of a cylinder}&=\pi r^2\times h\\[5pt]
&=154\times 24\\[5pt]
&=\underline{\underline{3696cm^3}}\\
\end{align}$ |
 | $\begin{align}(ii)&\text{When the radius is constant, the volume doubles and }\\[5pt]
&\text{triples as the height doubles and triples}\\[5pt]
&\text{When the radius is constant, if the height is changes by h ,}\\[5pt]
&\text{the volume also changes by h.}\\[5pt]
\end{align}$ |
 |
$\begin{align}(a)\text{Area of the cross section}&=\pi r^2\\[5pt]
&=\frac{22}{7}\times 7\times 7\\[5pt]
&=22\times 7\\[5pt]
&=\underline{\underline{154cm^2}}\\
\end{align}$
$\begin{align}\text{Volume of a cylinder}&=\pi r^2\times h\\[5pt]
&=154\times 20\\[5pt]
&=\underline{\underline{3080cm^3}}\\
\end{align}$ | $\begin{align}(b)\text{Area of the cross section}&=\pi r^2\\[5pt]
&=\frac{22}{7}\times 14\times 14\\[5pt]
&=22\times 2\times 14\\[5pt]
&=\underline{\underline{616cm^2}}\\
\end{align}$
$\begin{align}\text{Volume of a cylinder}&=\pi r^2\times h\\[5pt]
&=616\times 20\\[5pt]
&=\underline{\underline{12320cm^3}}\\
\end{align}$ |
$\begin{align}(c)\text{Area of the cross section}&=\pi r^2\\[5pt]
&=\frac{22}{7}\times 21\times 21\\[5pt]
&=22\times 3\times 21\\[5pt]
&=\underline{\underline{1386cm^2}}\\
\end{align}$
$\begin{align}\text{Volume of a cylinder}&=\pi r^2\times h\\[5pt]
&=1386\times 20\\[5pt]
&=\underline{\underline{27720cm^3}}\\
\end{align}$ | |
 | $\begin{align}(ii)&\text{When the height is constant, the volume is quadrupled}\\[5pt]
&\text{and nine times when the radius is doubled and tripled}\\[5pt]
&\text{When the height is constant, if the radius is changes by r ,}\\[5pt]
&\text{the volume also changed by r}^2\\[5pt]
\end{align}$ |
 |
$\begin{align}&\text{r=14cm , V=6160}cm^3, \text{h=?}\\[5pt]
\text{Volume of the water}&=\pi r^2\times h\\[5pt]
6160&=\frac{22}{7}\times 14\times 14\times h\\[5pt]
6160&=11\times 2\times 14\times h\\[5pt]
h&=\frac{6160}{11\times 2\times 14}\\[5pt]
h&=\frac{560}{28}\\[5pt]
&=\underline{\underline{20cm}}\\
\end{align}$ | |
 |
 | |
 |
$\begin{align}&\text{r=10cm ,h=?}\\[5pt]
\text{Area of the curved surface}&=1000cm^2\\[5pt]
2\pi rh&=1000\\[5pt]
1000&=2\times\frac{22}{7}\times 10\times h\\[5pt]
h&=\frac{100\times 7}{2\times 22}\\[5pt]
h&=\frac{700}{44}\\[5pt]
\text{Area of the cylinder}&=\pi r^2\times h\\[5pt]
&=\frac{22}{7}\times 10\times 10\times \frac{700}{44}\\[5pt]
&=\frac{10000}{2}\\[5pt]
&=\underline{\underline{5000cm^3}}\\
\end{align}$ | |
 |
$\begin{align}&\text{No of metal cylinders =n}\\[5pt]
\frac{1}{2}\times \pi r^2h&=n\times \pi r_1^2h_1\\[5pt]
\frac{1}{2}\times \pi \times \frac{21}{2} \times \frac{21}{2} \times 30&=n\times \pi \times \frac{7}{2} \times \frac{7}{2} \times 21\\[5pt]
\frac{21\times 15}{7\times 7}&=n\\[5pt]
n&=\frac{45}{7}\\[5pt]
h&=6\frac{3}{7}\\[5pt]
&=\underline{\underline{\text{6 metal cylinders can be made}}}\\
\end{align}$ | |
 |
$\begin{align}\text{Volume of water in cylindrical container}&=\pi r^2\times h\\[5pt]
&=\pi\times 14\times 14\times 30\\[5pt]
\text{Small cylindrical container capacity}&=\pi r^2\times h\\[5pt]
&=\pi\times 7\times 7\times 10\\[5pt]
\text{No of vessels required to remove water completely}&=\frac{\pi \times 14\times 14\times 30}{\pi\times 7\times 7\times 10}\\[5pt]
&=2\times 2\times 3\\[5pt]
&=\underline{\underline{12}}\\
\end{align}$ | |