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 $3$ , the cap's height is $7$ , and the cap's radius is $2$ . What is the object's volume?

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Answer 1 · 2018-02-16T08:33:56

see a step process below;

Using this formula;

$"vol of the spherical cap" + "volume of the prism" = "volume of the object"$

The spherical cap will take the shape of an hemisphere
Vol of hemisphere $=2/3πr^3$

The square prism will take d shape of a cube,
Vol of a cube $=l^3$

Vol of the object $=2/3πr^3 + l^3$

Vol of the object $= (2/3π xx 2^3) + (7^3)$

Vol of the object $= (2/3π xx 8) + 343$

Vol of the object $= 16/3π + 343$

Taking $LCM$

Vol of the object $= 16/3π + 343/1$

Vol of the object $=(16 + 1029)/3π$

Vol of the object $= 1045/3π$

Hope this helps!

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 3 3 , the cap's height is 7 7 , and the cap's radius is 2 2 . What is the object's volume?