Chef Potato's body has a cylinder in the middle and two half spheres that make up his bottom and head. He has the two dimensional shape measurements as follows: 20 cm in total length, 5 cm between the end of the cylinder and the top of the top sphere.
1.) Reduce Chef Potato by a scale factor of 0.5
2.) Chef Potato needs to be converted from a two dimensional shape to a three dimensional object and then enlarged to 300% of his original size. The three dimensional chef potato is similar in shape to a capsule made of a half sphere at the top, and a half sphere at the bottom and a cylinder in between.
A.Determine the surface area of the enlarged three dimensional chef potato and the scale factor
B.Determine the volume of the enlarged three dimensional chef potato
so, what in my previous response made it impossible for you to resolve the issues this time? What is still unclear? What have you tried so far?
To solve these questions, we need to apply some geometry formulas for finding the surface area and volume of various shapes.
1.) Reduce Chef Potato by a scale factor of 0.5:
If we reduce Chef Potato by a scale factor of 0.5, it means that all dimensions of Chef Potato will be halved.
Given measurements:
Total length = 20 cm
Distance between end of the cylinder and top of top sphere = 5 cm
To calculate the new measurements after reducing by a scale factor of 0.5:
Total length_reduced = Total length * Scale factor = 20 cm * 0.5 = 10 cm
Distance_reduced = Distance * Scale factor = 5 cm * 0.5 = 2.5 cm
So, the reduced Chef Potato has:
Total length_reduced = 10 cm
Distance between the end of the cylinder and the top of the top sphere_reduced = 2.5 cm
2.) Convert Chef Potato from 2D to 3D and enlarge it to 300% of its original size:
To calculate the surface area and volume of the enlarged three-dimensional Chef Potato, we need to calculate the dimensions of the shapes involved.
Given measurements for the original Chef Potato:
Total length = 20 cm
Distance between the end of the cylinder and the top of the top sphere = 5 cm
To convert to a capsule shape, we need to calculate the dimensions of the half spheres and the cylinder.
Radius of the top and bottom half spheres = Distance between the end of the cylinder and the top of the top sphere = 5 cm
Diameter of the top and bottom half spheres = 2 * Radius = 2 * 5 cm = 10 cm
Height of the cylinder = Total length - 2 * Radius = 20 cm - 2 * 5 cm = 10 cm
Enlarging the Chef Potato by 300% means multiplying all dimensions by 3.
Dimensions of the enlarged Chef Potato:
Diameter of the top and bottom half spheres_enlarged = Diameter of the top and bottom half spheres_original * Scale factor = 10 cm * 3 = 30 cm
Radius of the top and bottom half spheres_enlarged = Diameter_enlarged / 2 = 30 cm / 2 = 15 cm
Height of the cylinder_enlarged = Height of the cylinder_original * Scale factor = 10 cm * 3 = 30 cm
Scale factor = 3
A.) Determine the surface area of the enlarged three-dimensional Chef Potato:
The surface area of the enlarged Chef Potato can be calculated by summing the surface areas of the half spheres and the cylinder.
Surface area of half sphere = 2 * π * r^2
Surface area of cylinder = 2 * π * r * h
Surface area of enlarged Chef Potato = 2 * (Surface area of half sphere + Surface area of cylinder)
Surface area_enlarged = 2 * (2 * π * (15 cm)^2 + π * 2 * 15 cm * 30 cm)
Calculate the value:
Surface area_enlarged = 2 * (2 * π * 225 cm^2 + π * 30 cm * 15 cm)
B.) Determine the volume of the enlarged three-dimensional Chef Potato:
To find the volume of the enlarged Chef Potato, we need to calculate the volume of the half spheres and the cylinder.
Volume of half sphere = (4 / 3) * π * r^3
Volume of cylinder = π * r^2 * h
Volume of enlarged Chef Potato = Volume of half sphere + Volume of cylinder + Volume of half sphere
Volume_enlarged = (4 / 3) * π * (15 cm)^3 + π * (15 cm)^2 * 30 cm + (4 / 3) * π * (15 cm)^3
Calculate the value:
Volume_enlarged = (4 / 3) * π * 3375 cm^3 + π * 15 cm^2 * 30 cm + (4 / 3) * π * 3375 cm^3