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In this lesson, we will learn how to use formulas to solve problems in real-life contexts.

Q1:

The circumference of a circle as a function of its radius is given by πΆ ( π ) = 2 π π . Express the radius of a circle as a function of its circumference, denoting it by π ( πΆ ) , and then find π ( 3 6 π ) .

Q2:

Use the formula π΄ = 1 2 π β to determine the height, β , of a triangle given that its area, π΄ , is 4.5 and its base, π , is 2.

Q3:

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

Q4:

The volume, π , of a sphere with radius length π is given by π = 4 3 π π 3 . Find the radius length of a sphere with a volume of 4 . 8 5 1 Γ 1 0 3 cm^{3}. (Take π = 2 2 7 .)

Q5:

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

Q7:

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

Q8:

The volume, π , of a right circular cone with radius length π is given by π = 1 3 π π β ο¨ . Find the height of a right circular cone with volume 4β312 cm^{3} and base diameter length 28 cm. οΌ π = 2 2 7 . ο T a k e

Q9:

A roomβs temperature ranges from 2 5 β C to 3 0 β C . Determine its temperature range in degrees Fahrenheit, using the formula πΉ β 3 2 = 1 . 8 πΆ , where πΉ is the temperature in degrees Fahrenheit, and πΆ is the temperature in degrees Celsius.

Q10:

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

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