An object is made of a prism with a spherical cap on its square shaped top. The cap's base has a diameter equal to the length of the top. The prism's height is $9$ $9$ , the cap's height is $2$ $2$ , and the cap's radius is $4$ $4$ . What is the object's volume?

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An object is made of a prism with a spherical cap on its square shaped top. The cap's base has a diameter equal to the length of the top. The prism's height is $9$ $9$ , the cap's height is $2$ $2$ , and the cap's radius is $4$ $4$ . What is the object's volume?

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Answer 1 · 2017-11-12T01:50:56

$630.5$ $630.5$

Explanation:

The "tricky" part is really the sphere on top. The square dimension of the prism is also defined directly by the cap radius $(D = 2 \times r)$ $(D = 2 xx r)$ .
The base volume is simply $9 \times 8 \times 8 = 576$ $9 xx 8 xx 8 = 576$

The volume of the cap is : $V_{c} = \frac{1}{6} \times π \times h \times (3 \times a^{2} + h^{2})$ $V_c = 1/6 xx pi xx h xx (3 xx a^2 + h^2)$
$V_{c} = \frac{1}{6} \times π \times 2 \times (3 \times 4^{2} + 2^{2})$ $V_c = 1/6 xx pi xx 2 xx (3 xx 4^2 + 2^2)$

$V_{c} = 54.5$ $V_c = 54.5$
TOTAL Volume $= 576 + 54.5 = 630.5$ $= 576 + 54.5 = 630.5$

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An object is made of a prism with a spherical cap on its square shaped top. The cap's base has a diameter equal to the length of the top. The prism's height is $9$ $9$ , the cap's height is $2$ $2$ , and the cap's radius is $4$ $4$ . What is the object's volume?

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An object is made of a prism with a spherical cap on its square shaped top. The cap's base has a diameter equal to the length of the top. The prism's height is $9$ $9$ , the cap's height is $2$ $2$ , and the cap's radius is $4$ $4$ . What is the object's volume?