Mathematics Problem Set

Sarah is designing a cube-shaped garden box. If the volume of the box is 27 cubic feet, then the length of each side is expressed as a radical:

The area of a square playground is 50 square meters. The length of one side of the playground is:

Jake's science experiment involves doubling the number of bacteria every hour. If he starts with 5 bacteria, how many will there be after 6 hours? Express your answer in exponential form.

A triangular sail has an area of 24 square feet. If the base of the triangle is 8 feet, find the height, expressed as a simplified radical.

The volume of a spherical balloon is ⅓π(r³) cubic inches, where r is the radius. Given the volume is 36π cubic inches, determine the radius of the balloon expressed as a simplified radical.

Emily is calculating the diagonal of a rectangle. If the length is 12 cm and the width is 5 cm, what is the length of the diagonal expressed as a simplified radical?

The half-life of a radioactive element is 2 days, and starting with 64 grams, the amount remaining after 6 days is 8/1.

A company's profit doubles every year. If they made $10,000 in the first year, how much will they make in the 5th year? Express your answer in exponential form.

The area of an equilateral triangle is given by the formula A = (√3 / 4)a², where a is the length of a side. If the area is 16√3 square inches, choose the length of one side.

Tom is filling a cubic box with small cubes that have a side length of 2 inches. If the large box has a volume of 216 cubic inches, then the number of small cubes that can fit inside is: