Question

Create a sample drawing of a scale of a three-dimensional, real-world object. Then, determine the ratio of the surface areas. Upload your drawing and use complete sentences to explain how you determined the ratio.

Answer 1

Multiply the Surface Area of the Scale Drawing by the Square of the Scale Factor.

Explanation:

Given the sample scale drawing of a crate whose original dimensions are 150 cm by 200 cm by 250 cm.

The Scale Used is 1cm : 50cm

In any solid, the ratio of their areas is the square of the ratio of their sides.

Since it is a scale drawing, we take into cognizance the scale factor.

The ratio of the surface area is given as:

`2(3X4+4X5+3X5):2(3X4+4X5+3X5)X50^2\\=94:235000\\=1:2500`

To determine the ratio of their surface areas, follow these steps:

• Determine the Surface Area of the Scale Drawing
• Multiply the Surface Area of the Scale Drawing by the Square of the Scale Factor. In this case, our scale factor is 50cm, so we simply multiplied by
  `50^2`

Answer 2

Answer: S : B = 1 : 2

Explanation:

From the figure attached, the two cubes have length L

Starting from the small cube of L = 2 units

Since all sides are equal in a cube, the cube is of 2 units sides

The surface area of a cube = 6L^2

The surface area = 6(4) = 24 square units

The big cube of L = 4

That is double of the small cube unit sides.

The surface area = 6(16) = 96 square units

To determine the ratio of the surface areas of the two cubes, let the big cube = B and the small cube = S. Therefore

96/24 = B^2/ S^2

4 = (B/S)^2

B/S = 2

This means the ratio of B to S = 2:1

The ratio of the surface areas of the small cube to big cube can be expressed as

S:B = 1: 2

Please find the attached file for the figure