Surface Area of Cubes and Rectangular Prisms
How do you find the total surface area of a rectangular box?
A rectangular prism where all the sides are the same is a cube.
The surface area of a prism is the total sum of the areas of all its side faces. Representing a solid in two-dimensional form is called a net.
Surface area is the total area of all surfaces on a 3 – dimensional shape.
Cuboids or rectangular prisms have 6 rectangular faces.
We mark the length l, width w, and height h of the prism and use the formula,
Area of top and bottom face = 2 lw
Area of right and left side face = 2hw
Area of front and back face = 2hl
Example: Find the surface area of prism shown in the figure.
S = 2lw + 2lh + 2wh
= 2(3)(5) + 2(3)(6) + 2(5)(6)
= 30 + 36 + 60
= 126 square inches
Example: Find the surface area of an aquarium of dimensions 10 cm, 8 cm and 5 cm.
Formula for Surface area = 2lw + 2lh + 2wh
= 2.10.5 + 2.10.8 + 2.8.5
= 340 cm²
How do you find the surface area of a cube?
When all sides in a rectangular prism are equal, it is a cube. So, each face is a square.
A cube has 6 square faces.
In a cube all sides are equal so we calculate the surface area by 6 × side²
Example: Calculate the surface area of a cube of side 4 mm
Surface area of a cube = 6 × side²
= 6 × 4²
= 96 mm²
- Find the surface area of a rectangular wooden TV unit of length 18 cm, width 5 cm, height, 6 cm.
- Find the surface area of this cube.
- Aurora wants to calculate the surface area of a carton box which she needs to wrap. Length of the box is 7 cm, width is 5 cm, and 2 cm is the height.
- Find the surface area of a rectangular tube if the length, width, and height are as follows:
- Which of the following ice cubes will melt faster? “A” which measures 3 mm, 2 mm, 1 mm or “B” the other measures 2 mm, 1.5 mm, 1.3 mm. Calculate the surface area for both (Hint: the more is the surface area, the quicker it melts).
- What will be the surface area of cube with side 32 inches?
- 456 cm²
- 726 mm²
- 118 cm²
- 76 square inches
- A = 22 cm², B = 15.1 cm² A is the ice cube which will melt faster, due to larger surface area.
- 6,144 square inches