Find the surface area of basic 3D objects Geometry

The surface area is the sum of the areas of all faces. The cube has 6 square faces and the area of each face equals 9. Therefore, the surface area of the cube equals:

9 \times 6 = 54

The surface area of a cone with height h and radius r is equal to:

S=\pi r^2 + \pi r l

Where:

l=\sqrt{r^2+h^2}

Here, we have:

• r=2
• h=4
• l=\sqrt{20}=2\sqrt{5}

Therefore:

S=\pi \left(4\right)^2 + \pi \left(4\right) \sqrt{20}=16\pi+4\pi\sqrt{20}

The surface area of the cylinder equals:

S= 2 \pi r h + 2\pi r^2

Here, we have:

• r=2
• h=4

Therefore:

S= 2 \pi \left(2\right) \left(4\right) + 2\pi \left(2\right)^2=16\pi+8\pi = 24\pi

The surface area of the sphere with radius r equals:

S=4\pi r^2

Here, we have:

r=2

Therefore:

S=4\pi\left(2\right)^2 = 16\pi

The surface area of a rectangular cuboid with side lengths a,b and c equals:

S=2\left(ab + bc+ ac\right)

Here, we have:

• a=5
• b=6
• c=8

Therefore:

2\left[\left(5 \times 6\right) + \left(5 \times 8\right) + \left(6 \times 8\right)\right] = 236

The surface area of a cylinder with radius r and height h equals:

S=2\pi rh + 2\pi r^2

Here, we have:

• r=5
• h=20

S=2\pi \left(5\right)\left(20\right) + 2\pi \left(5\right)^2=250\pi

The surface area of a pyramid equals:

S=\dfrac{1}{2}px+B

Where p represents the perimeter of the base, x is the slant height, and B is the area of the base.

Here, we have:

• x=9
• B=8^2 = 64
• P=4 \times 8 = 32

S=\dfrac{1}{2}\left(32\right)\left(9\right)+64 = 208