volume and surface area of spheres and hemispheres

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

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 hemisphere?

Back

The volume V of a hemisphere is given by the formula V = (2/3)πr³, where r is the radius of the hemisphere.

Front

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

Back

The surface area A of a hemisphere is given by the formula A = 3πr², where r is the radius of the hemisphere.

Front

Calculate the volume of a sphere with a radius of 10 cm.

Back

V = (4/3)π(10)³ = 4188.79 cm³.

Front

Calculate the surface area of a sphere with a radius of 5 cm.

Back

A = 4π(5)² = 314.16 cm².

Front

If the radius of a sphere is doubled, how does the volume change?

Back

If the radius is doubled, the volume increases by a factor of 8 (since V = (4/3)π(2r)³ = 8 * (4/3)πr³).

Front

If the radius of a hemisphere is halved, how does the surface area change?

Back

If the radius is halved, the surface area decreases by a factor of 4 (since A = 3π(0.5r)² = 0.75πr²).

Front

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

Back

The volume of a sphere is directly related to the cube of its radius (V ∝ r³).

Front

What is the relationship between the radius and the surface area of a sphere?

Back

The surface area of a sphere is directly related to the square of its radius (A ∝ r²).