an ostrich egg has about the same volume as a sphere whith a diameter of 5 inches. If the eggshellis about 1/12 inch thick, find the volume

Question

an ostrich egg has about the same volume as a sphere whith a diameter of 5 inches. If the eggshellis about 1/12 inch thick, find the volume of just the shell, not including the interior of the egg. Round your answer to the nerest tenth.

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Caroline 4 weeks 2021-09-17T16:49:16+00:00 1 Answer 0

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    2021-09-17T16:50:59+00:00

    Answer:

    Volume of the shell is 6.3\ in^3.

    Step-by-step explanation:

    Given:

    diameter of the egg = 5 in

    radius of the egg r = \frac12 \times 5 = 2.5 \ in

    thickness of the shell = \frac{1}{12} \ in

    radius of interior without the shell = 2.5 - \frac{1}{12} = \frac{2.5\times 12}{12}- \frac{1}{12} = \frac{30}{12}- \frac{1}{12}= \frac{30-1}{12}=\frac{29}{12}\ in

    We need to find the volume of the shell.

    Solution:

    To find the volume of the shell we will subtract Volume of interior from Volume of the egg.

    first we will find the Volume of the egg.

    Now we know that;

    egg is in spherical form so we will use Volume of sphere.

    Volume of sphere is 4 by 3 times π times cube of the radius.

    framing in equation form we get;

    Volume of egg = \frac{4}{3}\pi r^3 = \frac{4}{3}\pi \times 2.5^3 \approx 65.45\ in^3

    Volume of interior = \frac{4}{3}\pi r^3 = \frac{4}{3}\pi \times (\frac{29}{12})^3 \approx 59.12\ in^3

    Volume of shell = Volume of egg – Volume of interior = 65.45-59.12 = 6.33\ in^3

    Rounding to nearest tenth we get;

    Volume of shell = 6.3\ in^3

    Hence Volume of the shell is 6.3\ in^3.

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