Volume of Solids of Revolution

The video tutorial explains how to find the volume of a solid of revolution by rotating a graph of y = x^2 around the y-axis, instead of the x-axis. It covers visualizing the resulting shape, calculating the volume using discs with depth in dy, and applying a definite integral to sum the volumes of these discs between y = 1 and y = 4. The process involves expressing x as a function of y and using the formula for the area of a circle to find the volume of each disc, ultimately leading to the final volume calculation.

What is the main difference in the approach to finding the volume of the solid in this video compared to previous ones?

• Using a different graph

• Rotating around the x-axis

• Changing the limits of integration

• Rotating around the y-axis

Tags

CCSS.7.G.A.3

What is the shape formed by rotating the graph around the y-axis compared to?

• An upside-down truffle

• A cylinder

• A cone

• A sphere

What is the purpose of constructing discs with depth in dy?

• To simplify the graph

• To find the volume of the solid

• To calculate the surface area

• To change the axis of rotation

Tags

CCSS.HSA-REI.B.4B

How is the radius of the disc expressed in terms of y?

• As y squared

• As the square root of y

• As y cubed

• As y divided by 2

Tags

CCSS.7.G.B.4

What is the formula for the area of the top of each disc?

• pi times y cubed

• pi times the square root of y

• pi times y squared

• pi times y

What is the next step after finding the area of the disc to determine the volume?

• Add to the radius

• Multiply by dx

• Multiply by dy

• Divide by dy

What is the purpose of evaluating the definite integral in this context?

• To find the surface area

• To approximate the volume

• To determine the radius

• To find the exact volume

What is the result of the definite integral for the volume of the solid?

• 8 times pi

• 15/2 times pi

• 15 times pi

• 7 and 1/2 times pi

What is the antiderivative of y used in the integral?

• y cubed over 3

• y squared over 2

• y divided by 2

• y squared

What are the limits of integration used to find the volume?

• 1 to 3

• 0 to 4

• 1 to 4

• 0 to 1