In this video, I discuss everything you must know about surface area and volume—including how to find the surface area and volume of cubes, rectangular prisms, spheres, pyramids, and cones—to do well on the Armed Services Vocational Aptitude Battery (ASVAB) or Pre-screening internet-delivered Computer Adaptive Test (PiCAT). Toward the end of the video, I also work out some challenging word problems that should closely mirror what you may see on the actual ASVAB or PiCAT.
0:00 Intro: No Calculator or Reference Sheet
1:52 Volume: Area of the Base of a Figure x Height of a Figure
2:21 Volume of a Cube: V = a^3, where a is any side of a cube
3:19 Volume of Rectangular Solid: V = l x w x h
3:54 Volume of a Cylinder: V = pi times r^2 times h
4:28 Volume of a Sphere: V = 4/3 times pi times r^3
4:46 Volume of a Rectangular Pyramid: V =1/3 times a times b times h
5:24 Volume of a Cone: V = 1/3 times r^2 times h
6:31 Surface Area of a Cube: SA = 6a^2
6:55 Surface Area of a Rectangular Solid: SA= 2lw + 2lh + 2wh
7:44 Easy Practice Question 1: Find Surface Area and Volume of a Cube
9:40 How to Derive the Formula for Surface Area of a Cube
12:15 Easy Practice Question 2: Find Surface Area and Volume of a Rectangular Solid
14:06 How to Derive the Formula for Surface Area of a Rectangular Solid
20:40 ASVAB/PiCAT Practice Question 1: Volume of a Rectangular Solid
22:18 ASVAB/PiCAT Practice Question 2: Volume of a Rectangular Solid
25:40 ASVAB/PiCAT Practice Question 3: Volume of a Rectangular Solid
29:17 ASVAB/PiCAT Practice Question 4: Surface Area of a Rectangular Solid
36:11 ASVAB/PiCAT Practice Question 5: Volume of a Rectangular Solid
40:05 ASVAB/PiCAT Practice Question 6: Volume of a Cylinder
45:05 ASVAB/PiCAT Practice Question 7: Volume and Surface Area of a Sphere
50:18 Outro: Like, Share, and Subscribe!
Iowa National Guard ASVAB Pretest:
https://www.iowanationalguard.com/Recruiting/Pages/default.aspx?url=https://www.iowanationalguard.com/Recruiting/Pages/pretest.htm
Take free ASVAB/PiCAT practice tests here: https://www.asvabapp.com/
Download my ASVAB/PiCAT reference sheet for free here: https://www.asvabapp.com/Reference.pdf
Download my ASVAB/PiCAT math checklist here:
https://www.asvabapp.com/checklist.pdf
Free Test Prep Resources for Mobile Devices
- U.S. Army ASVAB Challenge (Apple): https://apps.apple.com/us/app/u-s-army-asvab-challenge/id1496772113
- U.S. Army ASVAB Challenge (Android): https://play.google.com/store/apps/details?id=com.armygamestudio.usarec.asvab&hl=en_US&gl=US
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