The Fancy Marble Company makes one type of spherical marble with a radius of 2 cm. The maximum error in measurement is 0.1 cm for the radius. Which of the following is closest t…

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asked Sep 6, 2023 112k views

1 Answer

Serdar Dogruyol · Answer 1 · 2023-09-10T08:22:55+0000

hello

to solve this question, we need to find the volume of a sphere

the formula is given as

$\begin{gathered} v=(4)/(3)\pi r^3 \\ r=2\pm0.1 \\ \pi=3.14 \end{gathered}$

the minimum volume of the sphere is would be as a result in reduction of the radius of the sphere

$\begin{gathered} R=r-0.1 \\ R=2.0-0.1 \\ R=1.9\operatorname{cm} \end{gathered}$

we can use this radius to calculate the volume of the sphere

$\begin{gathered} v=(4)/(3)\pi R^3 \\ v=(4)/(3)*3.14*1.9^3 \\ v=28.716\cong28.72\operatorname{cm}^3 \end{gathered}$

from the calculations above, the minimum volume of the sphere is 28.72cm^3 which corresponds to option C