Topic 55.5 Surface Area and Volume of Spheres

Front

What is the formula for the volume of a sphere?

Back

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

A = 4πr², where r is the radius of the sphere.

Front

How do you find the radius of a sphere if you know the diameter?

Back

Radius (r) is half of the diameter (d): r = d/2.

Front

If a sphere has a volume of 31,400 mi³, what is the first step to find its surface area?

Back

First, use the volume formula to find the radius: r = ((3V)/(4π))^(1/3).

Front

What is density and how is it calculated?

Back

Density is mass per unit volume, calculated as Density = Weight/Volume.

Front

How do you convert diameter to radius?

Back

Divide the diameter by 2.

Front

What is the approximate surface area of a sphere with a radius of 10 cm?

Back

A = 4π(10)² ≈ 1256 cm².

Front

If a sphere has a radius of 5 in, what is its volume?

Back

V = (4/3)π(5)³ ≈ 523.6 in³.

Front

What is the relationship between volume and surface area in spheres?

Back

As the radius increases, both volume and surface area increase, but volume increases faster.

Front

How do you round numbers in calculations?

Back

Round to the nearest whole number by looking at the digit after the desired place value.