# Worksheet: Using Formulas to Solve Problems in Real-Life Contexts

Q1:

The circumference of a circle as a function of its radius is given by . Express the radius of a circle as a function of its circumference, denoting it by , and then find .

• A, 72
• B, 18
• C, 18
• D, 36
• E, 36

Q2:

The surface area, , of a sphere in terms of its radius, , is given by . Express as a function of and find, to the nearest tenth of an inch, the radius of a sphere whose surface area is 1000 square inches.

• A, 0.4 inches
• B, 0.1 inches
• C, 8.9 inches
• D, 2.5 inches
• E, 79.6 inches

Q3:

The volume, , of a cylinder with radius and height is . Given that a cylinder has a height of 6 meters, write an equation for the radius of the cylinder as a function of , and then use this to find the radius of the cylinder if its volume is 300 cubic meters. Give your answer to two decimal places.

• A, 2.25 meters.
• B, 69.10 meters.
• C, 3.99 meters.
• D, 0.92 meters.
• E, 15.92 meters.

Q4:

The volume of a right circular cone with radius and height is . First, write an equation for the radius of a cone with a height of 12 inches as a function of . Then, use this to find the radius of the cone to the nearest whole number given that its volume is 50 cubic inches.

• A, 9 inches
• B, 3 inches
• C, 2 inches
• D, 1 inch
• E, 4 inches

Q5:

Use the formula to determine the height, , of a triangle given that its area, , is 4.5 and its base, , is 2.

• A3
• B
• C
• D
• E

Q6:

The circumference of a circle can be estimated using the formula , where is the radius. Find an estimate of the radius of a circle with . Round your answer to the nearest tenth.

Q7:

The volume, , of a sphere with radius length is given by . Find the radius length of a sphere with a volume of cm3. (Take .)

Q8:

The volume, , of a right circular cone with radius length is given by . Find the height of a right circular cone with volume 4 312 cm3 and base diameter length 28 cm.

Q9:

A room’s temperature ranges from to . Determine its temperature range in degrees Fahrenheit, using the formula , where is the temperature in degrees Fahrenheit, and is the temperature in degrees Celsius.

• A to
• B to
• C to
• D to
• E to

Q10:

The surface area, , of a cylinder in terms of its radius, , and height, , is given by . Express the radius, , of a cylinder with a height of 4 feet as a function of . Find, to the nearest foot, the radius of such a cylinder whose surface area is 200 square feet.

• A, 7 feet
• B, 6 feet
• C, 4 feet
• D, 8 feet
• E, 6 feet