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
Give Your Child The eTutorWorld Advantage
Research has proven that personal online tutoring not just cements school learning, it helps build student confidence. eTutorWorld provides the best K-12 Online Tutoring Services so you can learn from the comfort and safety of your home at an affordable cost.
Be it an exam, class test or a quiz, eTutorWorld’s Math, Science and English tutors are responsible for your academic progress. Meet your personal coach at your convenient day and time to get help for Grade 3-12 Math, Science and English subjects and AP, SAT, SSAT and SCAT Test Prep help and test practice. All our tutors are graduates and bring with them years of teaching experience to the tutoring lessons.
Our ‘Learning by Design’ methodology makes sure that each student is at the center of the teaching-learning process. All tutoring sessions start with a question to the student ‘What do you want to learn today?’ Hence, tutors diagnose your skills and recognize your requirements before the actual tutoring happens. Post every tutoring session, an individualized worksheet is emailed to the student to assimilate learned concepts. Regular formative assessments are used to evaluate a student’s understanding of the subject.
The state of the art technology used is stable, user friendly and safe. All you need is a computer or a tablet and an internet connection. The easy-to-use web conferencing software requires a one time download, using which the student can talk and chat to the tutor, annotate on an interactive shared whiteboard or even share documents, assignments or worksheets.
All tutoring sessions are recorded and made available for a month so you can review concepts taught.
Email or call our support team with any issues or questions – we are here for you 24X7.
Also, download free printable math and science worksheets in pdf format and solve SCAT and SSAT Practice Tests online. Sign up for a Free Trial Lesson Today!
Thousands have taken the eTutorWorld Advantage – what are you waiting for?
© 2019 eTutorWorld - Online Tutoring and Test Prep | All rights reserved