# Worksheet: Changing the Subject of a Formula

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

**Q2: **

Rearrange to make the subject.

- A
- B
- C
- D
- E

**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.

- A
- B
- C
- D
- E

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

**Q8: **

Albert Einsteinβs 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.

- A
- B
- C
- D
- E

**Q9: **

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

- A
- B
- C
- D
- E

**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

**Q15: **

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

**Q16: **

A roomβs 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

**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 cm^{3}
and base diameter length
28 cm.
(Take .)

**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.

- A
- B
- C
- D
- E

**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.

- A
- B
- C
- D
- E

**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 .

- A
- B
- C
- D
- E

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

- A
- B
- C
- D
- E

**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 .

- A
- B
- C
- D
- E

**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