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 lengths of the top. The prism's height is $12$ $12$ , the cap's height is $8$ $8$ , 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 lengths of the top. The prism's height is $12$ $12$ , the cap's height is $8$ $8$ , and the cap's radius is $4$ $4$ . What is the object's volume?

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Answer 1 · 2018-08-11T10:11:41

$Volume of the object V_{o} = 512 + (\frac{256}{3}) π \approx 780.08 cubic units$ $color(purple)("Volume of the object " V_o = 512 + (256/3) pi ~~ color(chocolate)(780.08 " cubic units"$

Explanation:

$Prism's height H_{p} = 12, Radius of sphere R_{c} = 4, Height of cap H_{c} = 8 = D_{c} = 2 \cdot R_{c}$ $"Prism's height " H_p = 12, " Radius of sphere " R_c = 4, " Height of cap " H_c = 8 = D_c = 2 * R_c$

It's a sphere over square prism with side of square base and the diameter of sphere same. i.e. $S_{p} = D_{c} = 8$ $S_p = D_c = 8$

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$Volume of prism V_{p} = S_{p}^{2} \cdot H_{p} = 8 \cdot 2 \cdot 12 = 512$ $"Volume of prism " V_p = S_p^2 * H_p = 8*2 * 12 = 512$

$Volume of sphere V_{s} = \frac{4}{3} π R_{c}^{3} = \frac{4}{3} \cdot π \cdot 4^{3} = (\frac{256}{3}) π$ $"Volume of sphere " V_s = 4/3 pi R_c^3 = 4/3 * pi * 4^3 = (256/3) pi$

$Volume of the object V_{o} = V_{p} + V_{s} = 512 + (\frac{256}{3}) π \approx 780.08 cubic units$ $"Volume of the object " V_o = V_p + V_s = 512 + (256/3) pi ~~ 780.08 " cubic units"$

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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 lengths of the top. The prism's height is $12$ $12$ , the cap's height is $8$ $8$ , 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 lengths of the top. The prism's height is $12$ $12$ , the cap's height is $8$ $8$ , and the cap's radius is $4$ $4$ . What is the object's volume?