# 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 # 15 #, the cap's height is #8 #, and the cap's radius is #9 #. What is the object's volume?

Total volume

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To find the volume of the object, you calculate the volume of the prism and the volume of the spherical cap separately, then add them together.

The volume of the prism is given by V_prism = base area * height_prism. Since the prism's base is square-shaped with side length equal to the diameter of the cap's base, the base area is (2 * 9)^2 = 324 square units. Given the prism's height is 15 units, the volume of the prism is V_prism = 324 * 15 = 4860 cubic units.

The volume of the spherical cap is given by V_cap = (1/3) * π * h_cap^2 * (3R - h_cap), where h_cap is the height of the cap and R is the radius of the sphere from which the cap is cut. Given the cap's height is 8 units and its radius is 9 units, the volume of the cap is V_cap = (1/3) * π * 8^2 * (3*9 - 8) = (64/3) * π * (27 - 8) = (64/3) * π * 19 = 4057.33 cubic units (approximately).

Adding the volumes of the prism and the cap together gives the total volume of the object:

Total Volume = V_prism + V_cap = 4860 + 4057.33 ≈ 8917.33 cubic units.

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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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