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Worksheet: Using Formulas to Solve Word Problems

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:

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

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 , 0.92 meters.
  • B , 15.92 meters.
  • C , 69.10 meters.
  • D , 3.99 meters.
  • E , 2.25 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 , 1 inch
  • B , 4 inches
  • C , 3 inches
  • D , 2 inches
  • E , 9 inches

Q5:

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

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