Question

IF THE VOLUME OF HEMISPHERE IS 343 CM 3 FIND THE TOTAL SURFACE AREA


please it's urgent​

Answer 1

Answer:

• Exact surface area=$3\pi (\sqrt[3]{\frac{1058841}{4\pi ^{2} } } ) cm^{2}$

• To the nearest thousandth: 282.116 cm²

Step-by-step explanation:

The volume of a hemisphere is (2/3)πr³.

Set this equal to 343 to solve for the radius:

(2/3)πr³=343

(3/2)(2/3)πr³=(3/2)(343)

πr³=$\frac{1029}{2}$

r³=$\frac{1029}{2\pi }$

$\sqrt[3]{r^{3} } =\sqrt[3]{\frac{1029}{2\pi } }$

r=$\sqrt[3]{\frac{1029}{2\pi } }$

The surface area of a hemisphere is $3\pi r^{2}$. Plug the radius into the formula to solve for the surface area:

SA=$3\pi (\sqrt[3]{\frac{1029}{2\pi } } )^{2}$

SA=3$\pi$($\sqrt[3]{\frac{1058841}{4\pi ^{2} } }$)

To the nearest thousandth:

• SA=282.116 cm²