Geo B 9.6 Surface Area and Volume of Spheres

Front

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

Back

The surface area (A) of a sphere is given by the formula A = 4πr², where r is the radius.

Front

What is the formula for the volume of a sphere?

Back

The volume (V) of a sphere is given by the formula V = (4/3)πr³, where r is the radius.

Front

What is the relationship between the radius and diameter of a sphere?

Back

The diameter (d) of a sphere is twice the radius (r): d = 2r.

Front

How do you calculate the radius from the surface area of a sphere?

Back

To find the radius from the surface area, use the formula r = √(A/(4π)).

Front

How do you calculate the radius from the volume of a sphere?

Back

To find the radius from the volume, use the formula r = (3V/(4π))^(1/3).

Front

What is a great circle?

Back

A great circle is the largest circle that can be drawn on a sphere, dividing it into two equal halves.

Front

What is the surface area of a sphere with a radius of 3 ft?

Back

Using the formula A = 4πr², the surface area is A = 4π(3)² = 36π ft².

Front

What is the volume of a sphere with a radius of 2 cm?

Back

Using the formula V = (4/3)πr³, the volume is V = (4/3)π(2)³ = (32/3)π cm³.

Front

What is the surface area of a sphere with a diameter of 10 in?

Back

First, find the radius: r = 10/2 = 5 in. Then, A = 4π(5)² = 100π in².

Front

What is the volume of a sphere with a radius of 5 m?

Back

Using the formula V = (4/3)πr³, the volume is V = (4/3)π(5)³ = (500/3)π m³.