surface area and volume of spheres

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

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

Back

The volume V = (4/3)π(3)³ = 36π cm³ ≈ 113.10 cm³.

Front

If the radius of a sphere is 5 cm, what is its surface area?

Back

The surface area A = 4π(5)² = 100π cm² ≈ 314.16 cm².

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, so d = 2r.

Front

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

Back

Increasing the radius of a sphere increases its volume exponentially, as volume is proportional to the cube of the radius.

Front

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

Back

Increasing the radius of a sphere increases its surface area quadratically, as surface area is proportional to the square of the radius.

Front

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

Back

The volume V = (4/3)π(2)³ = (4/3)π(8) = (32/3)π cm³ ≈ 33.51 cm³.

Front

What is the surface area of a sphere with a radius of 1 cm?

Back

The surface area A = 4π(1)² = 4π cm² ≈ 12.57 cm².

Front

If a sphere has a volume of 904.78 cm³, what is its radius?

Back

To find the radius, use the formula r = ((3V)/(4π))^(1/3). For V = 904.78 cm³, r ≈ 6.24 cm.