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 # 7 #, the cap's height is #8 #, and the cap's radius is #8 #. What is the object's volume?

Answer 1

#color(maroon)("Volume of the object " = pi r^2 H + (2/3) pi r^3 ~~ 2479.7638 " cubic units"#

#"Volume of the object " = " Volume of cylindrical prism + Volume of spherical cap (or hemisphere)"#

#"Vol. of Spherical Cap " V_s = (2/3) pi r^3 " as " r = h#

#"Volume of Prism = V_p = pi r^2 H#

#"Given ' r = 8, H = 7#

#"Vol. of object " V_o = V_p + V_s#

#V_o = pi ^ 8^2 * 7 + (2/3) * pi * 8^3#

#color(maroon)(V_o = pi * 8^2 * ( 7 + 16/3) ~~ 2479.7638 " cubic units"#

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Answer 2

To find the volume of the object, first calculate the volume of the prism and then add the volume of the spherical cap.

Volume of prism = base area × height Base area of the prism = side length of square × side length of square Base area = (side length of square)² Height of prism = 7

Volume of prism = (side length of square)² × 7

Next, calculate the volume of the spherical cap.

Volume of spherical cap = (π/6) × h² × (3r - h)

Where: h = height of the cap r = radius of the cap

Given: h = 8 r = 8

Volume of spherical cap = (π/6) × 8² × (3×8 - 8)

Finally, add the volume of the prism and the volume of the spherical cap to find the total volume of the object.

Total volume = Volume of prism + Volume of spherical cap

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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