Adding and Subtracting Rational Expressions

This video tutorial covers the geometry of spheres, focusing on calculating both volume and surface area. It begins with an introduction to the parts of a sphere, including the center, radius, and great circle. The tutorial then provides detailed steps for calculating the volume of a sphere using the formula 4/3 πr³, followed by examples. Next, it explains how to calculate the surface area using the formula 4πr², with additional examples. The video concludes with application problems that apply these calculations to real-world scenarios, such as determining the material needed for a basketball or the volume of a box filled with spheres.

What defines a sphere in geometric terms?

• A two-dimensional circle expanded in three dimensions

• A cube with rounded edges

• A solid where all points are equidistant from a central point

• A shape with all points at equal distances from the edges

How is the volume of a sphere calculated?

• 4/3 PI R cubed

• PI R squared

• R squared divided by 3PI

• 2/3 PI R cubed

What is the volume of a sphere with a radius of 4 units?

• 268.1 cubic units

• 201.1 cubic units

• 150.8 cubic units

• 100.5 cubic units

What happens to the volume calculation if the radius is halved?

• It doubles

• It reduces to one-eighth

• It is halved

• It is quartered

What formula is used to calculate the surface area of a sphere?

• 4 PI R squared

• PI R cubed

• 6 PI R squared

• 2 PI R squared

Calculate the surface area for a sphere with a radius of 7 units.

• 615.8 square units

• 307.9 square units

• 1231.6 square units

• 154.95 square units

How does changing the radius affect the surface area of a sphere?

• It remains constant

• It decreases with increase in radius

• It increases fourfold with doubling of radius

• It increases proportionally with the square of the radius

What is the diameter of a sphere if its surface area is known to be 1017.88 square millimeters?

• 24 millimeters

• 18 millimeters

• 9 millimeters

• 36 millimeters

How much leather material is needed for a basketball with a circumference of 94.25 inches?

• 5654.8 square inches

• 1413.7 square inches

• 2827.4 square inches

• 707.85 square inches

Find the total volume of a composite solid consisting of a half-sphere and a cone, given the dimensions.

• 320.4 cubic feet

• 80.1 cubic feet

• 160.2 cubic feet

• 240.3 cubic feet