What are some formulas for surface area with lateral area included?
There are several formulas that involve surface area with lateral area included, depending on the shape of the object. Here are some common formulas:
1. Cylinder:
- Surface Area with Lateral Area = 2πrh + 2πr^2
(where r is the radius and h is the height of the cylinder)
2. Cone:
- Surface Area with Lateral Area = πrl + πr^2
(where r is the radius and l is the slant height of the cone)
3. Prism:
- Surface Area with Lateral Area = Ph + 2B
(where P is the perimeter of the base, h is the height of the prism, and B is the area of the base)
4. Pyramid:
- Surface Area with Lateral Area = (1/2)Pl + B
(where P is the perimeter of the base, l is the slant height of the pyramid, and B is the area of the base)
5. Frustum of a Cone:
- Surface Area with Lateral Area = π(r1 + r2)l + πr1^2 + πr2^2
(where r1 and r2 are the radii of the top and bottom bases, and l is the slant height of the frustum)
These formulas are applicable when you need to find the total surface area of a solid object, including both the lateral area and the surface area of the base(s).
1. Total Surface Area of a Right Circular Cylinder = 2πr² + 2πrh
2. Total Surface Area of a Right Prism = ph + 2B, where p is the perimeter of the base and B is the area of the base
3. Total Surface Area of a Square Pyramid = s² + 2s(l/2), where s is the length of the base and l is the slant height
4. Total Surface Area of a Cone = πr² + πrl, where r is the radius of the base and l is the slant height
5. Total Surface Area of a Sphere = 4πr²
6. Total Surface Area of a Rectangular Prism = 2lw + 2lh + 2wh