Worksheet: Formulas and Problem Solving

In this worksheet, we will practice 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 , 36
• B , 36
• C , 18
• D , 18
• E , 72

Q2:

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

• A
• B
• C
• D
• E3

Q3:

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.

Q4:

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

Q5:

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

Q6:

The volume, , of a cylinder with radius and height is . Given that a cylinder has a height of 6 metres, 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 , 0.92 metres.
• B , 15.92 metres.
• C , 69.10 metres.
• D , 3.99 metres.
• E , 2.25 metres.

Q7:

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

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