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 #4 #, and the cap's radius is #8 #. What is the object's volume?
It's a trickilywritten question: we need to deduce that it's a sphere on a square prism. It is also not clear whether the top is spherical or hemispherical. The volume of the object is
Volume of the sphere:
If the cap is a hemisphere, its volume will be half this,
The square has side length
Volume of square prism:
If the cap is a full sphere, the total volume is
If the cap is a hemisphere, the total volume is
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To find the volume of the object, you need to calculate the volumes of the prism and the spherical cap separately and then add them together.

Volume of the prism: Volume = base area × height Since the base is square, its area is the side length squared: Base area = (side length)^2 = (8)^2 = 64 square units Height of the prism = 7 units Volume of the prism = 64 square units × 7 units = 448 cubic units

Volume of the spherical cap: Given the cap's radius (r) is 8 units and height (h) is 4 units, you can use the formula for the volume of a spherical cap: Volume = (1/3)πh^2(3r  h) Volume of the cap = (1/3)π(4^2)(3(8)  4) = (1/3)π(16)(24  4) = (1/3)π(16)(20) = (320/3)π cubic units

Total volume of the object: Total volume = Volume of prism + Volume of cap Total volume = 448 cubic units + (320/3)π cubic units
So, the volume of the object is 448 cubic units + (320/3)π cubic units.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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