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. Reduce Chef
1.) 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. Determine the surface area of the enlarged three dimensional chef potato and the scale factor.
3.) What are possible dimensions of a box that could be used to deliver the enlarge model of chef potato to store? Justify your answer.
frist you reduce chef;
multiply all dimensions by .5
then for volume, dimentsions have to be cubed. 300percent is 3 times, so take all dimensions and multiply by cubr(3) and then that's 1.44
yep....
1.) To reduce Chef Potato by a scale factor of 0.5, we need to decrease all the dimensions of the figure by 0.5. Let's calculate the new measurements:
- Total length: 20 cm * 0.5 = 10 cm
- Distance between cylinder and top sphere: 5 cm * 0.5 = 2.5 cm
So the reduced dimensions of Chef Potato would be a total length of 10 cm and a distance of 2.5 cm between the end of the cylinder and the top of the top sphere.
2.) To determine the surface area of the enlarged three-dimensional Chef Potato and the scale factor when it is converted from a two-dimensional shape, we need to first calculate the dimensions of the new figure after enlarging it by 300% (3 times the original size).
Since the three-dimensional Chef Potato is similar in shape to a capsule, we can assume that the proportions of the dimensions will remain the same when enlarged.
Let's denote the scale factor as "k". The new dimensions can be calculated using the equation:
new dimension = k * original dimension
Here, we need to find the value of "k" when the figure is enlarged by 300% (or scale factor of 3).
Therefore,
k * original dimension = 3 * original dimension
k = 3
So, the scale factor is 3.
Now, let's calculate the new dimensions:
- Total length: 20 cm * 3 = 60 cm
- Distance between cylinder and top sphere: 5 cm * 3 = 15 cm
The new dimensions of the enlarged Chef Potato are a total length of 60 cm and a distance of 15 cm between the end of the cylinder and the top of the top sphere.
To calculate the surface area of the enlarged figure, we need to find the surface area of each component (two half spheres and the cylinder) and add them together.
- Surface area of a sphere = 4πr^2 (where r is the radius)
- Surface area of a cylinder = 2πrh + 2πr^2 (where r is the radius and h is the height)
Using the new dimensions, we can calculate the surface areas of the half spheres and the cylinder. Then, add them together to get the surface area of the enlarged Chef Potato.
3.) To determine the dimensions of a box that could be used to deliver the enlarged model of Chef Potato to a store, we need to find the dimensions of the enlarged Chef Potato.
As calculated previously, the new dimensions of the enlarged Chef Potato are a total length of 60 cm and a distance of 15 cm between the end of the cylinder and the top of the top sphere.
To determine the possible dimensions of a box, we should consider the length, width, and height of the enlarged Chef Potato.
The length of the box can be the same as the total length of the Chef Potato, which is 60 cm.
For the width and height of the box, we need to consider the maximum dimensions of the Chef Potato.
The maximum width of the Chef Potato would be the diameter of the largest component, which is the sphere at the bottom. The diameter can be calculated as twice the radius of the sphere:
Diameter = 2 * radius = 2 * (15 cm / 2) = 15 cm
Similarly, the maximum height of the Chef Potato would be the sum of the heights of both half spheres and the cylinder:
Height = 15 cm + 15 cm + 60 cm = 90 cm
Therefore, the possible dimensions of a box that could be used to deliver the enlarged model of Chef Potato to a store would be 60 cm (length) x 15 cm (width) x 90 cm (height).
1.) To reduce Chef Potato by a scale factor of 0.5, we need to multiply all of its measurements by 0.5.
- The total length will become 20 cm * 0.5 = 10 cm.
- The distance between the end of the cylinder and the top of the top sphere will become 5 cm * 0.5 = 2.5 cm.
Therefore, the reduced dimensions of Chef Potato will be a total length of 10 cm and a distance of 2.5 cm between the end of the cylinder and the top of the top sphere.
2.) To determine the surface area of the enlarged three-dimensional Chef Potato, we need to calculate the surface area of each individual shape and then add them together.
- The surface area of a sphere is calculated using the formula 4πr^2, where r is the radius. In this case, the radius is half of the total length, so it is 10 cm / 2 = 5 cm. Thus, the surface area of each sphere is 4 * π * (5 cm)^2 = 4π * 25 cm^2 = 100π cm^2.
- The surface area of a cylinder is calculated using the formula 2πrh, where r is the radius and h is the height. In this case, the radius is 5 cm, and the height is the total length minus the combined height of the two spheres, which is 10 cm - (2 * 5 cm) = 10 cm - 10 cm = 0 cm. Thus, the surface area of the cylinder is 2π * 5 cm * 0 cm = 0 cm^2.
To calculate the surface area of the enlarged three-dimensional Chef Potato, we add the surface areas of the two spheres and the cylinder:
- Surface area = 2 * (100π cm^2) + 0 cm^2 = 200π cm^2.
The scale factor of the enlargement is 300% or 3 times the original size.
3.) To determine the possible dimensions of a box that could be used to deliver the enlarged model of Chef Potato, we need to consider the largest dimensions of the enlarged model.
- The largest dimensions will be double the radius of the sphere. Since the original total length was 20 cm, the radius of each sphere will be 20 cm / 2 = 10 cm.
Therefore, the possible dimensions of the box should have at least a length, width, and height of 20 cm, to allow for the largest dimensions of the enlarged model of Chef Potato.