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.

1. reduce chef;

multiply all dimensions by .5

2. for volume, dimentsions have to be cubed. 300percent is 3 times, so take all dimensions and multiply by cubr(3) (duh, that's 1.44)

1.) To reduce Chef Potato by a scale factor of 0.5, we will need to multiply all of his dimensions by 0.5.

Given the original total length of 20 cm, when scaled down by 0.5, the new total length will be:
20 cm * 0.5 = 10 cm

For the distance between the end of the cylinder and the top of the top sphere, scaled down by 0.5, it will be:
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 convert Chef Potato from a two-dimensional shape to a three-dimensional object, we will create a capsule shape. Since Chef Potato's body consists of a cylinder in the middle and two half spheres for the bottom and head, the three-dimensional object will have a similar structure.

First, let's find the surface area of the enlarged three-dimensional Chef Potato.

To enlarge the three-dimensional Chef Potato to 300% of its original size, we need to multiply all of its dimensions by 3.

Given that the original dimensions are:
- Total length: 20 cm
- Distance between the end of the cylinder and the top of the top sphere: 5 cm

After scaling up by 300%, the new dimensions will be:
- Total length: 20 cm * 3 = 60 cm
- Distance between the end of the cylinder and the top of the top sphere: 5 cm * 3 = 15 cm

The surface area of a capsule can be calculated using the formula:
Surface area = 2πr^2 + πd * (2r)

For the top and bottom half spheres, the radius will be half of the distance between the end of the cylinder and the top of the top sphere. So, the radius will be 15 cm / 2 = 7.5 cm.

For the cylinder, the radius will be the same as the radius of the spheres, while the height will be the total length minus the diameter of the spheres. So, the radius will be 7.5 cm, and the height will be 60 cm - 15 cm = 45 cm.

Now we can calculate the surface area:
Surface area = 2π(7.5)^2 + π(2 * 7.5)(45)
Surface area ≈ 3536.19 cm^2

Therefore, the surface area of the enlarged three-dimensional Chef Potato is approximately 3536.19 cm^2.

The scale factor for the enlargement is 3, as we multiplied all dimensions by 3.

3.) To determine possible dimensions of a box that could be used to deliver and store the enlarged model of Chef Potato, we need to consider the dimensions of the enlarged three-dimensional Chef Potato.

The dimensions of the enlarged three-dimensional Chef Potato are:
- Total length: 60 cm
- Distance between the end of the cylinder and the top of the top sphere: 15 cm

Based on these dimensions, we need to find a box that is large enough to accommodate the largest dimension, which is the total length of 60 cm.

A possible box dimension could be 70 cm (length) x 70 cm (width) x 70 cm (height). This provides enough space for the enlarged model of Chef Potato with some extra room for packaging materials and protection.

Alternatively, if a smaller box is preferred, a dimension of 65 cm (length) x 65 cm (width) x 65 cm (height) could also work.

In justifying the choice of these possible dimensions, it's important to ensure that the box is large enough to fit the enlarged model of Chef Potato without being too tight or risking damage during transportation.

1.) To reduce Chef Potato by a scale factor of 0.5, we need to multiply all of the dimensions by 0.5. Since Chef Potato is formed by a cylinder and two half spheres, we need to individually scale each component.

The length of the cylinder is reduced to 20 cm * 0.5 = 10 cm.
The height of the top sphere is reduced to 5 cm * 0.5 = 2.5 cm.

So the reduced Chef Potato has a length of 10 cm and 2.5 cm between the end of the cylinder and the top of the top sphere.

2.) To convert Chef Potato from a 2D shape to a 3D object similar to a capsule, we need to add a cylinder in between the two half spheres.

To enlarge Chef Potato by 300%, we need to multiply all of the dimensions by 3. The half spheres and the cylinder have different dimensions, so we should calculate their individual measurements:

The top and bottom half spheres:
The original height of the top sphere is 5 cm. After enlarging by 300%, the new height becomes 5 cm * 3 = 15 cm.

The cylinder:
The original length of the cylinder is 20 cm. After enlarging by 300%, the new length becomes 20 cm * 3 = 60 cm.

Now, let's calculate the surface area of the enlarged three-dimensional Chef Potato:

Surface area of the top and bottom half spheres = 2 * π * r^2, where r is the radius of each half sphere.
The radius of each half sphere can be calculated by dividing the height of the respective half sphere by 2. Therefore, the radius of each half sphere is 15 cm / 2 = 7.5 cm.

Surface area of each half sphere = 2 * π * (7.5 cm)^2 = 2 * π * 56.25 cm^2.

Total surface area of the half spheres = 2 * 2 * π * 56.25 cm^2 = 4 * π * 56.25 cm^2.

The surface area of the cylinder = 2 * π * r * h, where r is the radius of the cylinder and h is the height of the cylinder.
The radius of the cylinder is 7.5 cm, and the height of the cylinder is 60 cm.

Surface area of the cylinder = 2 * π * 7.5 cm * 60 cm.

Finally, the total surface area of the enlarged three-dimensional Chef Potato is the sum of the surface areas of the half spheres and the cylinder:

Total surface area = Total surface area of the half spheres + Surface area of the cylinder.

3.) To determine the possible dimensions for a box that could be used to deliver the enlarged Chef Potato model, we need to consider its overall size.

Since Chef Potato's enlarged model has a length of 60 cm, a height of 30 cm (sum of the heights of both half spheres), and a width of 15 cm (radius of each half sphere), the dimensions of the box should be greater than or equal to these measurements to accommodate the model and provide some extra space for padding or protection.

Therefore, one possible set of dimensions for the box could be: length ≥ 60 cm, height ≥ 30 cm, width ≥ 15 cm.

The dimensions of the box are chosen to ensure that the model will fit inside and have sufficient space for packaging material and protection during delivery.