Question

volume of cone 1232cm3 radius of the base 7cm to find total suface area

Answer 1

Hi there ;
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$\large{Good\: Afternoon}$

Above is the Solution ^_^

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✨✨BE BRAINLY✨✨

Answer 2

Given :

• Volume of cone = 1232 cm³
• Radius of base = 7 cm

To Find :

• Slant height of cone
• Total suface area of cone

Solution :

$\large\boxed { \tt \blue{ Volume_{Cone} = \dfrac{\pi {r}^{2}h }{3}} } \\ \\ \tt 1232 = \frac{22 \times \cancel{7} \times 7 \times h }{ \cancel{7} \times 3} \\ \\ \tt h = \frac{1232 \times 3}{22 \times 7} \\ \\ \tt h = \frac{3696}{154} \\ \\ \tt h = 24 \: cm$

By Using Pythagoras theorem :

$\tt {l}^{2} = {h}^{2} + {r}^{2} \\ \\ \tt {l}^{2} = {24}^{2} + {7}^{2} \\ \\ \tt {l}^{2} = 576 + 49 \\ \\ \tt l = \sqrt{625} \\ \\ \tt l = 25 \: cm$

Now we can find Total suface area of cone

$\large\boxed{ \tt \orange{TSA_{Cone} = \pi r(r + l)}} \\ \\ \implies \tt \frac{22 \times 7(7 + 25)}{7} \\ \\ \tt \implies \frac{22 \times \cancel 7 \times 32}{ \cancel7} \\ \\ \implies\tt 704 \\ \\ \large \boxed{ \tt \green{ TSA_{Cone} = 704 {cm}^{2} }}$