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!