Question

a cylinder has a diameter of 6 in. and a height of 19 in.
use \\( \pi = 3.14 \\).
\\( \boldsymbol{a} \\) what is the lateral surface area?
\\( \boldsymbol{b} \\) what is the total surface area?
the base of a triangular prism is a right triangle with a hypotenuse of 74 mm and legs that are...

Explanation:

Step1: Find the radius and formula for lateral surface area

The diameter \(d = 6\) in, so the radius \(r=\frac{d}{2}=\frac{6}{2}=3\) in. The formula for the lateral surface area of a cylinder is \(L = 2\pi rh\). Given \(h = 10\) in and \(\pi=3.14\).

$$L=2\times3.14\times3\times10$$

Step2: Calculate the lateral surface area

$$L = 6.28\times3\times 10=18.84\times10 = 188.4$$

square inches.

Step3: Formula for total surface area

The formula for the total surface area of a cylinder is \(T=2\pi r(r + h)\)

$$T=2\times3.14\times3\times(3 + 10)$$

Step4: Calculate the total surface area

First, \(3+10 = 13\). Then \(2\times3.14\times3\times13=6.28\times3\times13 = 18.84\times13=244.92\) square inches.

Answer:

a. The lateral surface area is \(188.4\) square inches.
b. The total surface area is \(244.92\) square inches.