Balls

Three metal balls with volumes V1=71 cm3 V2=78 cm3 and V3=64 cm3 melted into one ball. Determine it's surface area.

Result

S =  172.5 cm2

Solution:

V=V1+V2+V3=213 cm3 V=43πr3=213 cm3 r=34πV3=3.7 cm  S=4πr2=4π3.72=172.5 cm2V = V_1 + V_2 + V_3 = 213 \ cm^3 \ \\ V = \dfrac43 \pi r^3 = 213 \ cm^3 \ \\ r = \sqrt[3]{\dfrac3{4\pi} V } = 3.7 \ cm \ \\ \ \\ S = 4 \pi r^2 = 4 \pi \cdot 3.7^2 = 172.5 \ \text{cm}^2



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