A hand drum has a diameter of 14 7/8 inches and is 3 in deep. What is the amount of hide needed if the hide only covers top and lateral faces?
*what are lateral faces?
Thanks!
they are the sides of the drum. Their area is circumference * height.
Thanks
A hand drum has a diameter of 14 7/8 inches and is 3 in deep. What is the amount of hide needed if the hide only covers top and lateral faces?
To find the amount of hide needed to cover the top and lateral faces of a hand drum, we first need to understand what the lateral faces are.
Lateral faces refer to the side faces of a three-dimensional object, in this case, the hand drum. In other words, they are the vertical sides of the drum.
Now, let's calculate the surface area that needs to be covered with hide:
1. Calculate the area of the top face: The top face of the drum is circular, so we can calculate its area using the formula for the area of a circle:
Area = π * (radius)^2
Given that the diameter of the drum is 14 7/8 inches, the radius would be half of that. Let's convert the mixed fraction to an improper fraction:
Diameter = 14 7/8 inches = 14 + 7/8 = 14 + (7 ÷ 8) = (14*8 + 7)/8 = 119/8 inches
Radius = 119/8 inches ÷ 2 = 59.5/8 inches
Now we can calculate the area of the top face:
Top face area = π * (59.5/8 inches)^2
2. Calculate the area of the lateral faces: The lateral faces of the drum form a cylinder shape. The formula for the lateral area of a cylinder is:
Lateral area = height * circumference
Given that the depth of the drum is 3 inches, the height of the lateral faces would be 3 inches.
Also, the circumference of the lateral faces would be equal to the circumference of the top face because the drum has the same radius throughout.
So, circumference = 2π * radius
Now we can calculate the area of the lateral faces:
Lateral area = 3 inches * (2π * (59.5/8 inches))
3. Add the area of the top face and the area of the lateral faces to get the total surface area that needs to be covered with hide:
Total surface area = Top face area + Lateral area
Now that we have the total surface area, we can determine the amount of hide needed to cover it. However, the thickness of the hide is not given, so we cannot calculate the exact amount of hide required without that information.