Digital SAT MATH 2024

Front

What is the formula for the volume of a sphere?

Back

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.

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.

Front

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

Back

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.

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.

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.

Front

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

Back

Front

How do you derive the volume formula for a sphere?

Back

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

Front

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

Back

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