Find the surface area of each of the following a cube that is 4 cm by 4 cm by 4 cm. A right circular cylinder that is 6 cm by 12cm. A right circular prisim 8cm by 5 cm by 6 cm. A sphere that is 4cm a right circular cone that is 8cm by 6 cm.
Cube: As = (4 * 4)6 = 96cm^2.
Cube: As = (4 * 4)6 = 96cm^2.
Rt. Circular Cylinder:
As = (3.14r^2)2 ) + 6.28rh,
As = (3.14 * 3^2)2 + 6.28 * 3 * 12
As = 56.52 + 226.08 = 282.6cm^2.
Rt. Rectangular Prism:
As = (8 * 5)2 + (5 * 6)2 + (6 * 8)2,
As = 80 + 60 + 96 = 236cm^2.
Sphere: As = 4*3.14*r^2 = 4*3.14*2^2 =
50.3cm^2.
Rt. Circular cone:
As = 3.14r^2 + 3.14rs. s = sqrt(r^2 + h^2).
s = sqrt(64 + 36) = 10cm.
As = 3.14 * 4^2 + 3.14 * 4*10,
As = 50.27 + 125.66 = 175.9cm^2.
Your problems did not identify radius
or diameters.
To find the surface area of different geometric shapes, you can use specific formulas. Let's calculate the surface area for each of the given shapes:
1. Cube: A cube has six equal square faces. The length of each side of the cube is given as 4 cm. To find the surface area, we can use the formula: Surface Area = 6 * (Side Length)^2. Plugging the values, the equation becomes Surface Area = 6 * (4 cm)^2 = 6 * 16 cm^2 = 96 cm^2.
2. Right Circular Cylinder: A right circular cylinder has two circular faces and one curved surface. The radius of the circular base is given as 6 cm, and the height is given as 12 cm. To calculate the surface area, add the area of the two circular bases and the curved surface area together. Circular base area = π * (Radius)^2. Curved surface area = 2 * π * Radius * Height. Plugging the values, the equation becomes Surface Area = 2 * (π * (6 cm)^2) + (2 * π * 6 cm * 12 cm) = 432π cm^2 ≈ 1357.17 cm^2 (approximately).
3. Right Circular Prism: A right circular prism has two circular faces and three rectangular faces. The radius of the circular base is given as 8 cm, and the height is given as 5 cm. To calculate the surface area, add the area of the two circular bases and the area of the three rectangular faces together. Circular base area = π * (Radius)^2. Rectangular face area = Length * Width. Plugging the values, the equation becomes Surface Area = 2 * (π * (8 cm)^2) + (3 * (8 cm * 5 cm)) = 128π + 120 cm^2 ≈ 648.51 cm^2 (approximately).
4. Sphere: A sphere has a curved surface with no base. The radius of the sphere is given as 4 cm. To calculate the surface area, use the formula: Surface Area = 4 * π * (Radius)^2. Plugging the value, the equation becomes Surface Area = 4 * π * (4 cm)^2 = 64π cm^2 ≈ 201.06 cm^2 (approximately).
5. Right Circular Cone: A right circular cone has a circular base and a curved surface. The radius of the circular base is given as 8 cm, and the slant height (the distance from the tip of the cone to the edge of the base) is given as 6 cm. To calculate the surface area, add the area of the circular base and the curved surface area together. Circular base area = π * (Radius)^2. Curved surface area = π * Radius * Slant Height. Plugging the values, the equation becomes Surface Area = (π * (8 cm)^2) + (π * 8 cm * 6 cm) = 64π + 48π cm^2 = 112π cm^2 ≈ 351.86 cm^2 (approximately).
Hence, the surface areas for each of the given shapes are:
- Cube: 96 cm^2
- Right Circular Cylinder: 1357.17 cm^2 (approximately)
- Right Circular Prism: 648.51 cm^2 (approximately)
- Sphere: 201.06 cm^2 (approximately)
- Right Circular Cone: 351.86 cm^2 (approximately)