What is the formula for the surface area of a sphere?

The surface area of a sphere is given by the formula: $$A = 4\pi r^2$$ , where r is the radius of the sphere.

How do you derive the volume formula for a sphere?

The volume formula for a sphere can be derived using calculus, specifically by integrating the area of circular cross-sections.

What is the difference between a point and a line in geometry?

A point is a location in space with no dimensions, while a line is a one-dimensional figure that extends infinitely in both directions.

What is the definition of a mathematical equation?

A mathematical equation is a statement that asserts the equality of two expressions, typically containing variables and constants.

What does it mean to solve an equation?

To solve an equation means to find the value(s) of the variable(s) that make the equation true.

What is the importance of understanding variables in algebra?

Understanding variables is crucial in algebra as they represent unknown values that can change, allowing for the formulation of equations and expressions.

What is a linear equation?

A linear equation is an equation of the first degree, meaning it can be written in the form $$ax + b = 0$$ , where a and b are constants.

What is the purpose of using variables in mathematical expressions?

Variables are used in mathematical expressions to represent unknown values, allowing for generalization and the ability to solve problems.

Digital SAT MATH 2024 Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the formula for the volume of a sphere?

Back

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

2.

FLASHCARD QUESTION

Front

What does the variable 'x' represent in the equation x + 3y = 70?

Back

In the equation x + 3y = 70, 'x' represents the number of 1-point questions in the assignment.

Tags

CCSS.6.EE.B.6

3.

FLASHCARD QUESTION

Front

What does the variable 'y' represent in the equation x + 3y = 70?

Back

In the equation x + 3y = 70, 'y' represents the number of 3-point questions in the assignment.

Tags

CCSS.6.EE.B.6

4.

FLASHCARD QUESTION

Front

How do you calculate the volume of a sphere with a radius of 3 units?

Back

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

5.

FLASHCARD QUESTION

Front

What is the relationship between the radius and the volume of a sphere?

Back

The volume of a sphere increases with the cube of the radius, meaning if the radius doubles, the volume increases by a factor of eight.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

6.

FLASHCARD QUESTION

Front

What is the significance of the constant \pi in the volume formula of a sphere?

Back

The constant \pi (approximately 3.14) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter, and it is essential in calculations involving circles and spheres.

Tags

CCSS.7.G.B.4

7.

FLASHCARD QUESTION

Front

If the radius of a sphere is halved, how does the volume change?

Back

If the radius is halved, the volume of the sphere decreases to one-eighth of the original volume, since volume is proportional to the cube of the radius.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

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