Hollow sphere

The hollow ball's volume is 3432 cm3. What is its internal radius when the wall thickness is 3 cm?

Correct answer:

r =  8 cm

Step-by-step explanation:

V=3432 cm3 h=3 cm V = V1​ − V2​ V1​ = 4/3 ⋅  π ⋅  (r+h)3 V2​ = 4/3 ⋅  π ⋅  r3 3/4/π⋅ V = (r+h)3 − r3 k=3/4/π⋅ V=3/4/3.1416⋅ 3432≐819.3296 9r2+27r+27=819.3296  9r2+27r−792.33=0  a=9;b=27;c=−792.33 D=b2−4ac=272−4⋅9⋅(−792.33)=29252.8656 D>0  r1,2​=2a−b±D​​=18−27±29252.87​​ r1,2​=−1.5±9.501927 r1​=8.00192729 r2​=−11.00192729 r>0 r=[r1​]=[8.0019]=8=8 cm V1​=4/3π⋅ (r+h)3=4/3⋅ 3.1416⋅ (8+3)3≐5575.2798 V2​=4/3π⋅ r3=4/3⋅ 3.1416⋅ 83≐2144.6606 V3​=V1​−V2​=5575.2798−2144.6606≐3430.6192

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