A birthday cake is being made using a cylindrical baking pan. The radius of the pan is 4 inches, and the height is 5 inches. Which formula represents the correct way to calculate the volume of the cake?
$V=(4)(5)$
$V=\pi(4)(5)$
$V=\pi(4)^2(5)$
$V=\pi(5)^2(4)$
Answer (2)
Recall the formula for the volume of a cylinder: V = π r 2 h .
Substitute the given radius r = 4 inches and height h = 5 inches into the formula: V = π ( 4 2 ) ( 5 ) .
Simplify the expression: V = π ( 16 ) ( 5 ) = 80 π .
The correct formula representing the volume of the cake is: V = π ( 4 ) 2 ( 5 ) .
Explanation
Problem Analysis We are given a cylindrical baking pan with a radius of 4 inches and a height of 5 inches. We need to find the correct formula to calculate the volume of the cake, which is the volume of the cylinder.
Recall the Volume Formula The formula for the volume of a cylinder is given by: V = π r 2 h where r is the radius and h is the height of the cylinder.
Substitute Values We are given that the radius r = 4 inches and the height h = 5 inches. Substituting these values into the formula, we get: V = π ( 4 ) 2 ( 5 ) V = π ( 16 ) ( 5 ) V = π ( 80 ) So, the volume of the cake is 80 π cubic inches.
Compare with Options Now, let's compare our calculated formula with the given options:
Option 1: V = ( 4 ) ( 5 ) = 20 Option 2: V = π ( 4 ) ( 5 ) = 20 π Option 3: V = π ( 5 ) 2 ( 4 ) = π ( 25 ) ( 4 ) = 100 π Option 4: V = r ( 4 ) 2 ( 5 ) = 16 ( 5 ) r = 80 r . This option is not correct because it includes 'r' in the final formula, and it should be a numerical value.
Comparing these with our result V = π ( 4 ) 2 ( 5 ) = 80 π , we see that Option 3 is the closest, but it has the radius and height swapped. Option 2 is 20 π , which is incorrect. The correct formula is V = π ( 4 ) 2 ( 5 ) . However, we need to choose the option that represents the correct formula, even if it's not fully simplified.
Final Answer The correct formula to calculate the volume of the cake is: V = π ( 4 ) 2 ( 5 ) This corresponds to the expression π ( 4 ) 2 ( 5 ) .
Examples
Understanding the volume of a cylinder is useful in many real-life situations. For example, when filling a cylindrical water tank, you need to know its volume to determine how much water is required. Similarly, in manufacturing, calculating the volume of cylindrical containers helps in packaging and storage. Also, when designing cylindrical structures like pillars or support beams, knowing the volume helps in estimating the material needed and the overall cost.
The correct formula to calculate the volume of the cake in a cylindrical baking pan is V = π ( 4 ) 2 ( 5 ) . This represents the volume calculation based on the radius of 4 inches and height of 5 inches. Therefore, the correct choice is the third option.
;
