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 :

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

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

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

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

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

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

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

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

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