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Deffense [45]
2 years ago
13

Easy points. this is due tomorrow, the formula is given but im not sure how to solve. help? x

Mathematics
1 answer:
ozzi2 years ago
4 0

\sf{\qquad\qquad\huge\underline{{\sf Answer}}}

Here we go ~

  • h = height of cone = 10 cm

  • r = radius of cone/sphere = ??

  • Volume of cone = 270 pi cm³

Volume of cone is :

\qquad \sf  \dashrightarrow \:v = 270 \pi

\qquad \sf  \dashrightarrow \: \dfrac{1}{3}   \cancel\pi {r}^{2} h = 270 \cancel\pi

\qquad \sf  \dashrightarrow \:r {}^{2}  \sdot10 = 270 \times 3

\qquad \sf  \dashrightarrow \: {r}^{2}  = 810 \div 10

\qquad \sf  \dashrightarrow \: { {r}^{2} }^{}  = 81

\qquad \sf  \dashrightarrow \:r =  \sqrt{81}

\qquad \sf  \dashrightarrow \:r = 9 \:  \: cm

Now, let's calculate volume of solid sphere with same radius is ~

\qquad \sf  \dashrightarrow \:vol =  \dfrac{4}{3}  \pi {r}^{3}

\qquad \sf  \dashrightarrow \:vol =  \dfrac{4} {3}   \sdot\pi \sdot  {9}^{3}

\qquad \sf  \dashrightarrow \:vol =  \dfrac{4} {3}   \sdot\pi \sdot  729

\qquad \sf  \dashrightarrow \:vol =  {4} {}    \sdot243 \sdot\pi

\qquad \sf  \dashrightarrow \:vol =  97 2\pi  \:  \:  {cm}^{3}

So, volume of the solid sphere in terms of pi is :

  • 972 pi cm³

<u>note</u> : the solid figure attached below the cone is a hemisphere, so if the volume of hemisphere is asked then just dovide the result for sphere by 2. that is :

  • 972pi / 2 = 486 pi cm³
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