# 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 length of the top. The prism's height is # 16 #, the cap's height is #1 #, and the cap's radius is #5 #. What is the object's volume?

This prism is square in shape; the width of the square is 10 due to the cap's radius of 5.

Prism volume:

Base area times height.

A spherical cap's volume is determined by:

Total amount:

By signing up, you agree to our Terms of Service and Privacy Policy

To find the volume of the object, we need to calculate the volumes of the prism and the spherical cap separately, and then add them together.

Volume of the prism: [V_{\text{prism}} = \text{Base area} \times \text{Height}]

The base of the prism is a square with side length equal to the diameter of the cap, which is twice the radius of the cap. So, the base area is: [A_{\text{base}} = (2 \times 5)^2 = 100]

Given that the height of the prism is 16 units, the volume of the prism is: [V_{\text{prism}} = 100 \times 16 = 1600]

Volume of the spherical cap: [V_{\text{cap}} = \frac{1}{3} \pi h^2 (3R - h)]

Given that the cap's height is 1 unit and the radius is 5 units, we can plug in these values: [V_{\text{cap}} = \frac{1}{3} \pi \times 1^2 \times (3 \times 5 - 1) = \frac{1}{3} \pi \times 1 \times 14 = \frac{14}{3} \pi]

Total volume of the object: [V_{\text{total}} = V_{\text{prism}} + V_{\text{cap}} = 1600 + \frac{14}{3} \pi]

By signing up, you agree to our Terms of Service and Privacy Policy

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.

- How can I find diameter of a circle?
- The vertices of triangle ABC are A(-4,0), B(2,4), and C(4,0). What is its area?
- 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?
- What is the perimeter of a rectangle with sides 2/9 m and 5/6 m?
- The base of a triangle is 4 cm greater than the height. The area is 30 cm^2. How do you find the height and the length of the base?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7