Question

find the area of a circle with a diameter of 8 inches.

1. what is the surface area of the prism? 5 in. 5 in. 4 in. 6 in. 3 in.

Explanation:

Step1: Find radius of the circle

The radius $r$ of a circle is half of the diameter $d$. Given $d = 8$ inches, so $r=\frac{d}{2}=\frac{8}{2}=4$ inches.

Step2: Calculate area of the circle

The formula for the area of a circle is $A=\pi r^{2}$. Substitute $r = 4$ into the formula: $A=\pi\times4^{2}=16\pi\approx 16\times 3.14 = 50.24$ square - inches.

Step3: Find area of triangular bases of the prism

The base of the prism is a triangle with base $b = 3$ inches and height $h = 4$ inches. The area of a triangle is $A_{t}=\frac{1}{2}bh$. So $A_{t}=\frac{1}{2}\times3\times4 = 6$ square inches. Since there are 2 triangular bases, the total area of the bases is $2A_{t}=2\times6 = 12$ square inches.

Step4: Find area of rectangular faces of the prism

There are 3 rectangular faces.

• For the face with dimensions 3 inches and 6 inches, its area $A_{1}=3\times6 = 18$ square inches.
• For the face with dimensions 4 inches and 6 inches, its area $A_{2}=4\times6 = 24$ square inches.
• For the face with dimensions 5 inches and 6 inches, its area $A_{3}=5\times6 = 30$ square inches.

The total area of the rectangular faces is $A_{r}=18 + 24+30=72$ square inches.

Step5: Calculate surface - area of the prism

The surface area of the prism $S$ is the sum of the area of the bases and the area of the rectangular faces. So $S=12 + 72=84$ square inches.

Answer:

The area of the circle is approximately $50.24$ square inches. The surface area of the prism is $84$ square inches.