# 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 = 2*hw*

Area of front and back face = 2*hl*

*Example: *Find the surface area of prism shown in the figure.

*Example:*

**S = 2 lw + 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.

*Example:*

Formula for Surface area **= **2*lw* + 2*lh* + 2*wh*

= 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

*Example:*

Surface area of a cube = 6 × side²

= 6 × 4²

= 96 mm²

**Check point **

- 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?

##### Answer key

- 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

+1-269-763-4602

+1-269-763-5024

Quick Links

Follow Us

#### Give Your Child The eTutorWorld Advantage

Research has proven that personal online tutoring not just cements school learning, it helps build student confidence. Come to eTutorWorld for Expert Tutors and best K-12 Online Tutoring Services in the comfort and safety of your home at an affordable cost. Find a tutor online for Grade 3-12 Math, Science and English subjects and AP, SAT, SSAT and SCAT Test Prep help and test practice. Get free printable math and science worksheets in pdf format and SCAT Practice Tests. Sign up for a Free Trial Lesson Today!

© 2018 eTutorWorld - Online Tutoring and Test Prep | All rights reserved