Volume/Surface Area STAAR Word Problems

Front

What is the formula for the volume of a cylinder?

Back

The volume V of a cylinder can be calculated using the formula V = πr²h, where r is the radius and h is the height.

Front

How do you calculate the volume of a cone?

Back

The volume V of a cone is calculated using the formula V = (1/3)πr²h, where r is the radius of the base and h is the height.

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

How do you find the surface area of a cylinder?

Back

The surface area A of a cylinder is calculated using the formula A = 2πr(h + r), where r is the radius and h is the height.

Front

What is the relationship between the volume of a cone and a cylinder with the same base and height?

Back

The volume of the cone is one-third the volume of the cylinder.

Front

How do you calculate the volume of a sphere given its diameter?

Back

First, find the radius by dividing the diameter by 2. Then use the formula V = (4/3)πr³.

Front

What is the significance of π in volume and surface area calculations?

Back

π (pi) is a constant approximately equal to 3.14159, used in formulas involving circles and 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

How do you convert the volume of a shape from cubic inches to cubic feet?

Back

To convert from cubic inches to cubic feet, divide the volume in cubic inches by 1,728 (since 1 cubic foot = 1,728 cubic inches).

Front

What is the volume of a cylinder with a radius of 3 feet and a height of 5 feet?

Back

Using the formula V = πr²h, the volume is V = π(3)²(5) = 45π cubic feet, approximately 141.37 cubic feet.