SAT Saturday: Geometry, Cone Volume, & Circle Equations

August 29, 2026

SAT Saturday: Geometry, Circles & Volume

A desk top full of geometry supplies – grid paper, pencils, pen, highlighter, protractor, eraser – ready to complete homework. — Image by Nic Rosenau via Unsplash

Welcome to Week #18 of SAT Saturday! Approximately 15% of the SAT Math section focuses on Geometry and Trigonometry. This area tests your understanding of area and volume formulas, line and angle relationships, right-triangle trigonometry, and equations of circles. Today, we are reviewing last week’s Problem-Solving and Data Analysis solutions before diving into cone volumes and completing the square for circles!

📝 Week #18 Practice Questions: Geometry & Circles

Question 35: Cone Volume Formula

A paper cone used for snow cones has a diameter of 8 cm and a height of 6 cm. What is the maximum volume of ice the cone can hold in cubic centimeters?

A) 32π cm³
B) 48 π cm³
C) 64 π cm³
D) 96 π cm³

Question 36: Standard Equation of a Circle (Grid-In Style) Completing the Square (Hard Module): The equation of a circle in the -plane is shown below:

x² + y² – 8x + 10y = 8

What is the radius of the circle?

(Work through your calculations! Full step-by-step solutions will be revealed in next week’s SAT Saturday post.)

Quick SAT Math Tip for Week #18

Geometry & Circle Cheat Sheet:

Volume of a Cone: V = (1/3)r²h (Note: Always remember to convert diameter to radius, so r = d/2!)
Standard Form of a Circle: (x – h)² + (y – k)² = r²
- (h, k) is the center of the circle.
- r² is on the right side, so take the square root of the constant to find the radius r!

🏆 Week #17 Answer Key & Detailed Explanations

Let’s review the step-by-step solutions for last week’s Ratios and Percentages questions.

Question 33: Percentages (Part of a Whole)

A shipment contains 8,000 chocolate bars, and 2,000 of them contain nuts. What percentage of the chocolate bars contains nuts?

A) 25%
B) 40%
C) 60%
D) 75%

Correct Answer: A) 25%

The Concept:

To find what percentage a part is of a whole, use the standard percentage formula:

Percentage = (Part/Whole)(100%)

Step-by-Step Breakdown:

Identify the Part and Whole:
- Part = 2,000 (chocolate bars with nuts)
- Whole = 8,000 (total chocolate bars)
Calculate: Percentage = 2,000 / 8,000 = 2/8 = ¼ = 0.25
Convert to a percentage: 0.25 x 100% = 25%.

Accordion #2

Question: A group of 24 students was polled about biology and chemistry classes:

Which ratio statement is true?

A) Ratio of enjoy biology to enjoy chemistry is 7:8.
B) Ratio of enjoy chemistry to don’t enjoy chemistry is 9:4.
C) Ratio of enjoy biology to don’t enjoy chemistry is 7:2.
D) Ratio of don’t enjoy biology to enjoy chemistry is 5:9.

Correct Answer: D) Ratio of don’t enjoy biology to enjoy chemistry is 5:9.

Step-by-Step Breakdown:

Let’s check each option using the data table:

Class Subject	Enjoys	Doesn’t Enjoy	Total
Biology	14	10	24
Chemistry	18	6	24

Option A: Enjoy Biology (14) to Enjoy Chemistry (18) ⇒ 14:18 = 7:9 (Incorrect; option says 7:8).
Option B: Enjoy Chemistry (18) to Don’t Enjoy Chemistry (6) ⇒18:6 = 3:1 (Incorrect; option says 9:4).
Option C: Enjoy Biology (14) to Don’t Enjoy Chemistry (6) ⇒ 14:6 = 7:3 (Incorrect; option says 7:2).
Option D: Don’t Enjoy Biology (10) to Enjoy Chemistry (18) ⇒ 10: 18 = 5:9 (Correct!).

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Geometry and coordinate geometry questions can quickly swallow up precious test time if you don’t know the algebraic shortcuts!

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