An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
Calculate the radius of each fencepost: r a d i u s = 2 1 = 0.5 feet.
Calculate the lateral surface area of one fencepost: L a t er a l S u r f a ce A re a = 2 × 3.14 × 0.5 × 7 = 21.98 square feet.
Calculate the area of the top of one fencepost: A re a = 3.14 × ( 0.5 ) 2 = 0.785 square feet.
Calculate the total surface area of all 11 fenceposts and round to the nearest hundredth: 250.42 square feet.
Explanation
Identify Given Information First, let's identify the given information:
Height of each fencepost: 7 feet
Diameter of each fencepost: 1 foot
Number of fenceposts: 11
Value of pi: 3.14
We need to find the total surface area of all 11 fenceposts to determine how much paint Ellis needs.
Calculate the Radius Next, we calculate the radius of each fencepost. The radius is half of the diameter: r a d i u s = 2 d iam e t er = 2 1 = 0.5 feet
Calculate Lateral Surface Area Now, we calculate the lateral surface area of one fencepost. The formula for the lateral surface area of a cylinder is: L a t er a l S u r f a ce A re a = 2 π r h
Substituting the values, we get: L a t er a l S u r f a ce A re a = 2 × 3.14 × 0.5 × 7 = 21.98 square feet
Calculate Top Surface Area We also need to calculate the area of the top circular surface of one fencepost. The formula for the area of a circle is: A re a = π r 2
Substituting the values, we get: A re a = 3.14 × ( 0.5 ) 2 = 3.14 × 0.25 = 0.785 square feet
Calculate Total Surface Area of One Post Now, we calculate the total surface area of one fencepost by adding the lateral surface area and the area of the top: T o t a l S u r f a ce A re a ( o n e p os t ) = L a t er a l S u r f a ce A re a + A re a o f T o p T o t a l S u r f a ce A re a ( o n e p os t ) = 21.98 + 0.785 = 22.765 square feet
Calculate Total Surface Area of All Posts Next, we calculate the total surface area of all 11 fenceposts: T o t a l S u r f a ce A re a ( a ll p os t s ) = 11 × T o t a l S u r f a ce A re a ( o n e p os t ) T o t a l S u r f a ce A re a ( a ll p os t s ) = 11 × 22.765 = 250.415 square feet
Round to Nearest Hundredth Finally, we round the total area to the nearest hundredth: R o u n d e d T o t a l A re a = 250.42 square feet
Therefore, Ellis will need 250.42 square feet of paint to paint all the surfaces of the 11 fenceposts.
Examples
Understanding surface area calculations is crucial in many real-world applications. For instance, when planning a construction project, accurately estimating the amount of material needed, such as paint for walls or fabric for upholstery, can save time and money. Surface area calculations are also vital in fields like packaging design, where minimizing material usage reduces costs and environmental impact. Furthermore, in environmental science, calculating the surface area of leaves helps determine the rate of photosynthesis in plants, contributing to climate change research.
