Keith is wrapping ribbon around a cylindrical vase he will need additional ribbon to make a bow the vase has a volume of 602.88 cubic inches the bow requires 3 feet of ribbon to the nearest inch what is the least amount of ribbon including the bow does Keith needs to wrap the vase?please show the steps u took to solve the problem.thank you.

Question

Keith is wrapping ribbon around a cylindrical vase he will need additional ribbon to make a bow the vase has a volume of 602.88 cubic inches the bow requires 3 feet of ribbon to the nearest inch what is the least amount of ribbon including the bow does Keith needs to wrap the vase?please show the steps u took to solve the problem.thank you.

Answer 1

To find the least amount of ribbon Keith needs to wrap the vase, we need to calculate the length of ribbon required to wrap around the cylindrical surface of the vase and add the length of ribbon needed for the bow. Here are the steps to solve the problem:

Step 1: Find the circumference of the vase
The formula for the circumference of a cylinder is C = 2πr, where C is the circumference and r is the radius of the base. Since we have the volume of the vase, we can calculate the radius using the formula V = πr²h, where V is the volume, r is the radius, and h is the height of the vase. Rearranging this formula, we get r = √(V / (πh)). Plugging in the given volume V = 602.88 cubic inches, and assuming the height h is known (but not given in the question), find the value of r.

Step 2: Calculate the circumference
Using the formula C = 2πr, substitute the value of r calculated in the previous step to find the circumference of the vase.

Step 3: Find the length of ribbon needed to wrap the vase
Multiply the circumference (found in Step 2) by the number of times the ribbon needs to go around the vase. Since the ribbon is wrapped around a cylindrical vase, we assume it goes around once completely. So, the length of ribbon needed to wrap the vase is equal to the circumference.

Step 4: Calculate the length of ribbon needed for the bow
The bow requires 3 feet of ribbon, which is approximately 36 inches.

Step 5: Add the lengths obtained in Steps 3 and 4 to find the total length of ribbon
Add the length of ribbon needed to wrap the vase (found in Step 3) and the length of ribbon needed for the bow (found in Step 4). Round the result to the nearest inch to get the least amount of ribbon Keith needs to wrap the vase.

By following these steps, you should be able to calculate the least amount of ribbon that Keith needs to wrap the vase.