Question

A rectangular prism has a height of 8cm, a length of 4cm, and a width of 3cm. The prism is enlarged by a scale of 2. Find the surface area ratio of the enlarged prism to the original prism

Answer 1

The area of enlarged prism is 4 times surface area of original prism.

Explanation:

We have been given that a rectangular prism has a height of 8 cm, a length of 4 cm, and a width of 3 cm. The prism is enlarged by a scale of 2.

Let us find total surface area of original prism as:

`SA_1=2(lw+wh+hl)`

`SA_1=2(4\text{ cm}(3\text{ cm})+3\text{ cm}(8\text{ cm})+8\text{ cm}(4\text{ cm}))`

`SA_1=2(12\text{ cm}^2+24\text{ cm}^2+32\text{ cm}^2)`

`SA_1=2(68\text{ cm}^2)`

`SA_1=136\text{ cm}^2`

Since the prism is enlarged by a scale of 2, so each side of new prism would be 2 times grater than side of original prism as:

Length: 8 cm

Width: 6 cm,

Height: 16 cm.

`SA_2=2(8\text{ cm}(6\text{ cm})+6\text{ cm}(16\text{ cm})+16\text{ cm}(8\text{ cm}))`

`SA_2=2(48\text{ cm}^2+96\text{ cm}^2+128\text{ cm}^2)`

`SA_2=2(272\text{ cm}^2)`

`SA_2=544\text{ cm}^2`

Let us find ratio of surface area of the enlarged prism to the original prism as:

`(SA_2)/(SA_1)=(544)/(136)`

`(SA_2)/(SA_1)=(4)/(1)`

Therefore, the area of enlarged prism is 4 times surface area of original prism.