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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 𝐢 ( π‘Ÿ ) = 2 πœ‹ π‘Ÿ . Express the radius of a circle as a function of its circumference, denoting it by π‘Ÿ ( 𝐢 ) , and then find π‘Ÿ ( 3 6 πœ‹ ) .

  • A π‘Ÿ ( 𝐢 ) = 𝐢 2 πœ‹ , 36
  • B π‘Ÿ ( 𝐢 ) = 𝐢 πœ‹ , 36
  • C π‘Ÿ ( 𝐢 ) = 𝐢 πœ‹ , 18
  • D π‘Ÿ ( 𝐢 ) = 𝐢 2 πœ‹ , 18
  • E π‘Ÿ ( 𝐢 ) = 𝐢 2 πœ‹ , 72

Q2:

The surface area, 𝐴 , of a sphere in terms of its radius, π‘Ÿ , is given by 𝐴 ( π‘Ÿ ) = 4 πœ‹ π‘Ÿ 2 . Express π‘Ÿ as a function of 𝐴 and find, to the nearest tenth of an inch, the radius of a sphere whose surface area is 1000 square inches.

  • A π‘Ÿ = √ 𝐴 4 πœ‹ , 2.5 inches
  • B π‘Ÿ = 𝐴 4 πœ‹ , 79.6 inches
  • C π‘Ÿ = ο„ž 4 πœ‹ 𝐴 , 0.1 inches
  • D π‘Ÿ = ο„ž 𝐴 4 πœ‹ , 8.9 inches
  • E π‘Ÿ = 4 πœ‹ √ 𝐴 , 0.4 inches

Q3:

The volume, 𝑉 , of a cylinder with radius π‘Ÿ and height β„Ž is 𝑉 = πœ‹ π‘Ÿ β„Ž 2 . Given that a cylinder has a height of 6 meters, write an equation for the radius of the cylinder as a function of 𝑉 , 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 π‘Ÿ = √ 𝑉 6 πœ‹ , 0.92 meters.
  • B π‘Ÿ = 𝑉 6 πœ‹ , 15.92 meters.
  • C π‘Ÿ = 𝑉 √ 6 πœ‹ , 69.10 meters.
  • D π‘Ÿ = ο„ž 𝑉 6 πœ‹ , 3.99 meters.
  • E π‘Ÿ = 1 πœ‹ ο„ž 𝑉 6 , 2.25 meters.

Q4:

The volume of a right circular cone with radius π‘Ÿ and height β„Ž is 𝑉 = 1 3 πœ‹ π‘Ÿ β„Ž 2 . First, write an equation for the radius of a cone with a height of 12 inches as a function of 𝑉 . Then, use this to find the radius of the cone to the nearest whole number given that its volume is 50 cubic inches.

  • A π‘Ÿ = ο„ž 𝑉 3 6 πœ‹ , 1 inch
  • B π‘Ÿ = 𝑉 4 πœ‹ , 4 inches
  • C π‘Ÿ = ο„ž πœ‹ 𝑉 3 6 , 3 inches
  • D π‘Ÿ = ο„ž 𝑉 4 πœ‹ , 2 inches
  • E π‘Ÿ = πœ‹ 𝑉 3 6 , 9 inches

Q5:

Use the formula 𝐴 = 1 2 𝑏 β„Ž to determine the height, β„Ž , of a triangle given that its area, 𝐴 , is 4.5 and its base, 𝑏 , is 2.

  • A 2 1 4
  • B 1 4 5
  • C 3 3 5
  • D 4 1 2
  • E3

Q6:

The circumference 𝐢 of a circle can be estimated using the formula 𝐢 = 4 4 7 π‘Ÿ , where π‘Ÿ is the radius. Find an estimate of the radius of a circle with 𝐢 = 6 7 . 1 . Round your answer to the nearest tenth.

Q7:

The volume, 𝑉 , of a sphere with radius length π‘Ÿ is given by 𝑉 = 4 3 πœ‹ π‘Ÿ 3 . Find the radius length of a sphere with a volume of 4 . 8 5 1 Γ— 1 0 3 cm3. (Take πœ‹ = 2 2 7 .)

Q8:

The volume, 𝑉 , of a right circular cone with radius length π‘Ÿ is given by 𝑉 = 1 3 πœ‹ π‘Ÿ β„Ž 2 . Find the height of a right circular cone with volume 4 312 cm3 and base diameter length 28 cm. ο€Ό πœ‹ = 2 2 7 .  T a k e

Q9:

A room’s temperature ranges from 2 5 ∘ C to 3 0 ∘ C . Determine its temperature range in degrees Fahrenheit, using the formula 𝐹 βˆ’ 3 2 = 1 . 8 𝐢 , where 𝐹 is the temperature in degrees Fahrenheit, and 𝐢 is the temperature in degrees Celsius.

  • A 6 2 ∘ F to 8 6 ∘ F
  • B 6 2 ∘ F to 3 4 7 ∘ F
  • C 8 6 ∘ F to 3 4 7 ∘ F
  • D 7 7 ∘ F to 8 6 ∘ F
  • E 6 2 ∘ F to 7 7 ∘ F

Q10:

The surface area, 𝐴 , of a cylinder in terms of its radius, π‘Ÿ , and height, β„Ž , is given by 𝐴 = 2 πœ‹ π‘Ÿ + 2 πœ‹ π‘Ÿ β„Ž 2 . Express the radius, π‘Ÿ , of a cylinder with a height of 4 feet as a function of 𝐴 . Find, to the nearest foot, the radius of such a cylinder whose surface area is 200 square feet.

  • A π‘Ÿ = ο„ž 𝐴 + 8 πœ‹ 2 πœ‹ + 2 , 8 feet
  • B π‘Ÿ = ο„ž 𝐴 + 8 πœ‹ 2 πœ‹ βˆ’ 2 , 6 feet
  • C π‘Ÿ = ο„ž 𝐴 + 8 πœ‹ 2 πœ‹ + 2 , 6 feet
  • D π‘Ÿ = ο„ž 𝐴 + 8 πœ‹ 2 πœ‹ βˆ’ 2 , 4 feet
  • E π‘Ÿ = ο„ž 𝐴 βˆ’ 4 πœ‹ 2 πœ‹ + 2 , 7 feet