a cylindrical cake with radius 12cm and height 10cm has a slice cut out. The shape of the top of the slice is a sector of the circle that forms the top of the cake.
a) Calculate the area on top of the slice that has been cut out.
b) Calculate the volume of the cake that remains after the slice has been removed.
c) Calculate the surface area of the cake that remains after the slice has been removed.
You will have to tell us something about the sector cut out, either its sector angle or its arc length.
sector angle is 320 degrees
this is me nabiha named anonymous
To calculate the answers to these questions, we need to know the angle of the sector that forms the top of the slice. Let's call this angle θ.
a) To calculate the area on top of the slice that has been cut out, we need to find the area of the sector. The formula to find the area of a sector is:
Area = (θ/360) * π * r^2
Here, r is the radius of the cake, which is 12 cm. Since the formula requires the angle in degrees, θ needs to be converted from radians to degrees.
If we assume that the top of the slice is a complete circle, then the angle is 360 degrees. But since it is a sector, we need to subtract the angle of the remaining portion.
b) To calculate the volume of the cake that remains after the slice has been removed, we need to find the volume of a cylinder and then subtract the volume of the cut-out portion. The formula for calculating the volume of a cylinder is:
Volume = π * r^2 * h
Here, r is the radius of the cake (12 cm) and h is the height of the cake (10 cm). To find the volume of the cut-out portion, we need to multiply the area on top of the slice that has been cut out by the height of the slice.
c) To calculate the surface area of the cake that remains after the slice has been removed, we need to find the lateral surface area of the cylinder and subtract the area of the cut-out portion. The formula for calculating the lateral surface area of a cylinder is:
Lateral Surface Area = 2 * π * r * h
Here, r is the radius of the cake (12 cm) and h is the height of the cake (10 cm). To find the surface area of the cut-out portion, we need to add the area on top of the slice that has been cut out to the circumference of the circular section removed.
Now, I will perform the calculations using the given values.