Question

If the height and slant height of a cone are 21 cm and 28 cm respectively. Find its volume.

Answer 1

Answer:

The volume of cone is 3231.03 cubic cm .

Step-by-step explanation:

Given as :

The height of a cone = H = 21 cm

The slant height of cone = L = 28 cm

Let The volume of cone = V cubic cm

According to question

∵  slant height of cone = $\sqrt{height^{2}+ radius^{2} }$

Or, L = $\sqrt{H^{2}+R^{2} }$

Or, 28 = $\sqrt{21^{2}+R^{2} }$

Or, R² = 28² - 21²

Or, R² = 784 - 441

Or, R² = 343

∴   Radius = R = 18.5 cm

Again

∵ Volume of cone = $\dfrac{1}{3}$ × π × radius² × height

i.e  V =  $\dfrac{1}{3}$ × 3.14 × 343 × 21

∴  V = 3231.06 cm³

So, The volume of cone = V = 3231.03 cubic cm

Hence,  The volume of cone is 3231.03 cubic cm . Answer

Answer 2

$\huge{\underline{\underline{\mathrm{\purple{GIVEN:-}}}}}$

• Height of the cone(h) = 21 cm
• Slant height of the cone(l) = 28 cm

$\huge{\underline{\underline{\mathrm{\purple{NEED\:TO\:FIND:-}}}}}$

Find the volume of the cone = ?

$\huge{\underline{\underline{\mathrm{\purple{FORMULA \:USED:-}}}}}$

$\large{\boxed{\bf{\red{{l}^{2}={h}^{2}+{r}^{2}}}}}$

$\large{\boxed{\bf{\red{Volume\: of\: cone = \frac{1}{3}\timesπ{r}^{2}h}}}}$

$\huge{\underline{\underline{\mathrm{\purple{SOLUTION:-}}}}}$

To find the volume of cone, we need to find the radius of cone:-

Putting the given values in formula

$\implies$ $\large\bf{{l}^{2} = {h}^{2} + {r}^{2}}$

$\implies$ $\bf{{28}^{2} = {21}^{2} + {r}^{2}}$

$\implies$$\bf{784 = 441 + {r}^{2}}$

$\implies$ $\bf{784 - 441 = {r}^{2}}$

$\implies$ $\bf{{r}^{2} = 343}$

$\implies$ $\bf{r = \sqrt{343}}$

$\implies$ $\large\bf\blue{r= 7\sqrt7}$

Now, putting the given values in the formula of volume of cone

$\implies$ $\large\bf{ Volume \:of \: cone = \frac{1}{3}\times π {r}^{2} h}$

$\rm{Take\: π = \frac{22}{7}}$

$\implies$ $\bf{\frac{1}{3}\times\frac{22}{7}\times7\sqrt{7}\times7\sqrt{7}\times 21}$

$\implies$ $\large\bf{\frac{462\times343}{21}}$

$\implies$$\cancel\dfrac{158466}{21}$

$\implies$ $\large\bf\blue{7546}$

Thus, the volume of cone is 7546 cm³

$\large{\underline{\underline{\mathrm{\purple{FINAL\:ANSWER:-}}}}}$

$\huge{\boxed{\boxed{\mathrm{\red{Volume = 7546\: {cm}^{3}}}}}}$