12.6 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 of the sphere.

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 of the sphere.

Front

If the radius of a sphere is 3 ft, what is its surface area?

Back

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

Front

If the radius of a sphere is 3 ft, what is its volume?

Back

Using the formula V = (4/3)πr³, the volume is V = (4/3)π(3)³ = 36π ft³.

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 does increasing the radius of a sphere affect its surface area?

Back

The surface area increases with the square of the radius; if the radius doubles, the surface area increases by a factor of four.

Front

How does increasing the radius of a sphere affect its volume?

Back

The volume increases with the cube of the radius; if the radius doubles, the volume increases by a factor of eight.

Front

What is the surface area of a sphere with a radius of 5 cm?

Back

Using the formula A = 4πr², the surface area is A = 4π(5)² = 100π cm².

Front

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

Back

Using the formula V = (4/3)πr³, the volume is V = (4/3)π(5)³ = (500/3)π cm³.

Front

What units are used for measuring the surface area of a sphere?

Back

The surface area of a sphere is measured in square units, such as square meters (m²) or square feet (ft²).