Question

if the area of the base of cone is 770m² and the area of its curved surface is 814m² then find out its volume​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

area of the base = 770 sq m

$\pi {r}^{2} \: = 770 \: {m}^{2}$

$\frac{22}{7} {r}^{2} = 770$

${r}^{2} = 770\times \frac{7}{22}$

${r}^{2} = 70 \times \frac{7}{2}$

${r}^{2} = 45 \times 7$

${r}^{2} = 7 \times 7 \times 5$

$r = 7 \sqrt{5} m$

radius of base = 7√5 m

CSA = 814

$\pi \: rl = 814$

$\frac{22}{7} \times 7 \sqrt{5} \times l \: = 814$

$l = 814 \times \frac{7}{22 \times 7 \sqrt{5} }$

$l = \frac{37}{ \sqrt{5} }$

slant hight of cone l =37/√5 m

height h =

$h = \sqrt{ {l}^{2} + {r}^{2} }$

$h = \sqrt{ { (\frac{37}{ \sqrt{5} } })^{2} + {(7 \sqrt{5} })^{2} }$

$h = \sqrt{ \frac{1369}{5} + 49 \times 5 }$

$h = \sqrt{ \frac{1369 + 1225}{5} }$

$h = \sqrt{ \frac{2594}{5} }$