Mastering Volume Calculations in Calculus
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Questions and Answers

What is the formula for finding the area of a square?

$A = s^2$

What is the formula for finding the perimeter of a square?

$P = 4s$

What is the formula for finding the area of a rectangle?

$A = wh$

What is the formula for finding the perimeter of a rectangle?

<p>$P = 2w + 2h$</p> Signup and view all the answers

What is the formula for finding the area of a triangle?

<p>$A = \frac{1}{2}bh$</p> Signup and view all the answers

How is a circle usually classified?

<p>A circle is usually classified by its radius, measured from the center of the circle to the edge.</p> Signup and view all the answers

What is the formula for the area of a circle?

<p>The formula for the area of a circle is $A = \pi r^2$.</p> Signup and view all the answers

What are the two ways to classify 3D shapes?

<p>The two ways to classify 3D shapes are shapes that are the same from top to bottom, and shapes that aren't the same from top to bottom.</p> Signup and view all the answers

What is the formula for finding the volume of a cylinder?

<p>The formula for finding the volume of a cylinder is $V = h \cdot A_{\text{base}}$, where $A_{\text{base}}$ is the area of the base of the cylinder.</p> Signup and view all the answers

What is the formula for finding the volume of a sphere?

<p>The formula for finding the volume of a sphere is $V = \frac{4}{3} \pi r^3$.</p> Signup and view all the answers

What are the two ways to classify 3D shapes?

<p>Shapes that are the same from the top to the bottom and shapes that aren't the same from the top to the bottom.</p> Signup and view all the answers

What is an example of a shape that is the same from the top to the bottom?

<p>A cylinder.</p> Signup and view all the answers

What is an example of a shape that is not the same from the top to the bottom?

<p>A square pyramid.</p> Signup and view all the answers

What is the shape of the cross-section of a cylinder?

<p>A circle.</p> Signup and view all the answers

What is the shape of the cross-section of a cube?

<p>A square.</p> Signup and view all the answers

What is the shape of the cross-section of a prism?

<p>A triangle.</p> Signup and view all the answers

What is the shape of the cross-section of a square pyramid?

<p>A square.</p> Signup and view all the answers

What is the shape of the cross-section of a regular pyramid?

<p>A triangle.</p> Signup and view all the answers

What is the shape of the cross-section of a sphere?

<p>A circle.</p> Signup and view all the answers

What happens when you slice through a sphere at the top?

<p>You get a little, teeny, tiny circle.</p> Signup and view all the answers

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