
Understanding the Volume of a Sphere

Interactive Video
•
Mathematics, Science
•
9th - 12th Grade
•
Hard

Liam Anderson
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the initial step in deriving the volume of a sphere using integration?
Graphing a circle and rotating it about the x-axis
Calculating the surface area of a sphere
Applying the formula for the volume of a cylinder
Using the Pythagorean theorem
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the volume of a vertical slice of the sphere represented?
As a square
As a right circular cylinder
As a rectangle
As a triangle
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What mathematical concept is introduced to express the sum of the volumes of the disks?
Differential equations
Algebraic expressions
Calculus notation
Trigonometric functions
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What change is made to the limits of integration to simplify the calculation?
Integrating from zero to r and multiplying by two
Integrating from zero to infinity
Integrating from negative r to zero
Integrating from negative infinity to infinity
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What substitution is performed to integrate with respect to x?
y = x^2
x^2 = y^2 + r^2
y^2 = r^2 - x^2
x = y^2
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the significance of multiplying the integral by two in the derivation?
To account for the entire sphere
To simplify the equation
To adjust for the radius
To convert units
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the antiderivative of the function used to find the volume of the sphere?
r^2 times x minus x cubed divided by three
x cubed minus r squared
x squared plus y squared
r cubed divided by three
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