Write the surface area of the sphere as a function of the 体積. Use this function to determine the surface area of a sphere with a 体積 of 125 cm3.

解

W r i t e t h e s u r f a ce a re a o f t h e s p h ere a s a f u n c t i o n o f t h e v o l u m e . U se t hi s f u n c t i o n t o d e t er min e t h e s u r f a ce a re a o f a s p h ere w i t h a v o l u m e o f 125 c m 3.

s u r f a ce a re a : 25 \cdot 3^{\frac{2}{3}} \cdot 4^{\frac{1}{3}} π^{\frac{1}{3}} c m^{2}

十進法表記

120.89939 \dots

解答ステップ

Given:

v o l u m e : 125 c m^{3}

指定された球体の半径

V o l u m e = 125 : r = \frac{5 3 3}{3 4 3 π}

指定された球体の表面積

r = \frac{5 3 3}{3 4 3 π} : A = 25 \cdot 3^{\frac{2}{3}} \cdot 4^{\frac{1}{3}} π^{\frac{1}{3}}

s u r f a ce a re a : 25 \cdot 3^{\frac{2}{3}} \cdot 4^{\frac{1}{3}} π^{\frac{1}{3}} c m^{2}