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Digital SAT · Solve it in Desmos

How to Solve Volume and Surface Area on Desmos (Digital SAT)

The calculator shines on backward problems and any pi-heavy arithmetic, since the equation resolves in a line. Choosing the formula and remembering to square the radius are the parts it leaves to you.

Perfect1600 Content Team·Uses the same Desmos calculator that is built into the Digital SAT

Full method for volume and surface area

The Desmos steps

  1. 1

    Enter the formula

    Type it with the numbers, such as pi*5^2*4 for a cylinder, and read the value.

  2. 2

    Invert for a missing side

    Set the formula equal to the known volume and let Desmos return the dimension.

  3. 3

    Keep pi exact

    Enter pi directly rather than a rounded decimal.

Open a real question in the same Desmos calculator you get on Perfect1600, with the setup already typed in:

Worked in Desmos

Easy example
A cube has an edge length of 3. What is the volume of the cube?
A
9
27
C
54
D
81

A: Incorrect. This squares the edge instead of cubing it.

B: Correct. The volume is 33=273^{3} = 27.

C: Incorrect. This doubles the correct volume.

D: Incorrect. This results from multiplying the volume by 3.

Explanation

Volume =33=27= 3^{3} = 27.

Medium example
A cylinder has a volume of 100π100\pi and a radius of 5. What is the height of the cylinder?
A
1
B
2
4
D
8

A: Incorrect. This results from dividing by 100π100\pi instead of 25π25\pi.

B: Incorrect. This results from using r=5r = 5 but dividing incorrectly.

C: Correct. From 100π=π(5)2h100\pi = \pi(5)^{2} h, h=100π25π=4h = \frac{100\pi}{25\pi} = 4.

D: Incorrect. This uses r=5r = 5 directly as a divisor rather than r2r^{2}.

Explanation

h=100π25π=4h = \frac{100\pi}{25\pi} = 4.

Detailed explanation

From 100π=π(5)2h100\pi = \pi(5)^{2} h, dividing by 25π25\pi gives h=4h = 4.

Hard example
A rectangular prism has dimensions 6 by 4 by xx and a volume of 96. What is the surface area of the prism?
A
96
B
112
128
D
160

A: Incorrect. This is the volume of the prism, not its surface area.

B: Incorrect. This omits one pair of faces from the surface-area sum.

C: Correct. Since x=4x = 4, the surface area is 2(6⋅4+6⋅4+4⋅4)=1282(6\cdot4 + 6\cdot4 + 4\cdot4) = 128.

D: Incorrect. This results from an error in summing the face areas.

Explanation

x=4x = 4; surface area =2(24+24+16)=128= 2(24 + 24 + 16) = 128.

Detailed explanation

Since 6×4×x=966 \times 4 \times x = 96, x=4x = 4; the surface area is 2(24+24+16)=1282(24 + 24 + 16) = 128.

Try it with the calculator

Question 1easy

A rectangular prism has a length of 4, a width of 3, and a height of 5. What is the volume of the prism?

Question 2easy

A cylinder has a radius of 2 and a height of 5. What is the volume of the cylinder?

Question 3 is ready when you are

Keep going with more questions of this type, each with the same step-by-step reasoning. Free to start.

Start the free diagnostic

Desmos questions

Can Desmos solve volume and surface area questions on the SAT?

The calculator shines on backward problems and any pi-heavy arithmetic, since the equation resolves in a line. Choosing the formula and remembering to square the radius are the parts it leaves to you.

Is the Desmos calculator really built into the Digital SAT?

Yes. The Bluebook testing app includes the Desmos graphing calculator on every Math question, so the method here is one you can use on test day, not a workaround.

Should I still learn the algebra?

Yes. Desmos is fastest when you know what to type and what to read. Learn the underlying method on the full guide, then use the calculator to move quickly and to check your work.

Master volume and surface area, calculator and all

Every Digital SAT question type comes with the method, the Desmos shortcut, and free practice with instant feedback.

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