# Worksheet: Changing the Subject of a Formula

In this worksheet, we will practice rearranging simple formulas using inverse operations.

Q1:

Solve with an expression for in terms of .

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Q2:

Rearrange to make the subject.

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Q3:

In 1897, Amos Dolbear derived a formula linking the number of cricket chirps and the temperature. The law states that the temperature , in degrees Celsius, is related to the number of cricket chirps in a minute by the formula

Rearrange the formula to make the subject.

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Given that the temperature on a particular day is , estimate the number of cricket chirps that you would expect to hear in a minute.

Q4:

The final velocity of an object with uniform acceleration can be calculated using the formula . Make the subject.

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Q5:

The displacement, , of an object traveling with uniform acceleration, , can be calculated using the formula , where is the initial velocity and is the time.

Make the subject.

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Calculate the acceleration of an object that has started from rest and traveled 200 m in 8 s.

Q6:

The variables and where is non-negative are related by the formula . Rewrite the formula with as the subject.

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Q7:

The variables and are related by the formula . Make the subject.

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Q8:

Albert Einstein’s famous formula , where the constant is the speed of light, relates the energy, , contained in matter and its mass, . Rearrange the formula to make the subject.

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Q9:

The variables and are related by the formula . Make the subject.

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Q10:

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.

Q11:

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, 18
• B, 72
• C, 36
• D, 18
• E, 36

Q12:

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

Q13:

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

Q14:

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

Q15:

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

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Q16:

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

Q17:

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

Q18:

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 1,000 square inches.

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

Q19:

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. (Take .)

Q20:

The formula for the circumference of a circle is . Rearrange this formula to make the subject.

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Q21:

Using the formulae for the circumference and area of a circle, eliminate the variable to find a formula that allows you to calculate the circumference of a circle from its area.

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Q22:

Using the formulae for the circumference and area of a circle, eliminate the variable to find a formula that allows you to calculate the area of a circle from its circumference.

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Q23:

The picture shows the design of a logo which is formed from two semicircles with a common center. Work out the perimeter of the logo, giving your answer in terms of .

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Work out the area of the logo, giving your answer in terms of .

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Q24:

The volume of a right circular cone in terms of its height and base radius is . Give a formula for the radius in terms of and .

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Q25:

A container holds 100 mL of a solution that is 25 mL acid. If mL of a solution that is acid is added, the function gives the concentration, , as a function of the number of milliliters added, . Express as a function of and determine the number of milliliters needed to have a solution that is acid.

• A, 50 mL
• B, 68 mL
• C, 250 mL
• D, 750 mL
• E, 23 mL