Question

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

Answer 1

`\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 \: (1)/(3) \cancel\pi {r}^(2) h = 270 \cancel\pi`

`\qquad \sf  \dashrightarrow \:r {}^(2) \sdot10 = 270 * 3`

`\qquad \sf  \dashrightarrow \: {r}^(2) = 810 / 10`

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

`\qquad \sf  \dashrightarrow \:r = √(81)`

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

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

`\qquad \sf  \dashrightarrow \:vol = (4)/(3) \pi {r}^(3)`

`\qquad \sf  \dashrightarrow \:vol = \frac{4} {3} \sdot\pi \sdot {9}^(3)`

`\qquad \sf  \dashrightarrow \:vol = \frac{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

note : 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