Question

what is the cross - section of a right cylinder that is perpendicular to the base?
circle
rectangle
square
triangle
question 10 (multiple choice worth 1 points)
(05.01r, 05.04r mc)
find the total surface area of a cylinder with a height of 7 cm and radius of 3 cm. leave your answer in terms of π.
14π cm²
91π cm²
60π cm²
51π cm²
question 11 (multiple choice worth 1 points)
(05.09r mc)
triangle lmn is an obtuse triangle with l = 5.2, n = 7, and m∠m = 121°. what is the area of δlmn? round your answer to the nearest tenth.
15.8 square units
18.2 square units
31.2 square units
36.4 square units

Explanation:

Step1: Identify cross-section shape

A right cylinder's base is a circle. A cross-section perpendicular to the base will have two sides equal to the cylinder's height, and two sides equal to the diameter of the base, forming a rectangle.

Step2: Recall total surface area formula

The total surface area of a cylinder is $SA = 2\pi r^2 + 2\pi r h$, where $r$ is radius and $h$ is height.

Step3: Substitute values for cylinder

$r=3$, $h=7$
$SA = 2\pi(3)^2 + 2\pi(3)(7) = 2\pi(9) + 42\pi = 18\pi + 42\pi = 60\pi$

Step4: Use triangle area formula

For $\triangle LMN$, use the formula $Area = \frac{1}{2} l n \sin(M)$

Step5: Substitute triangle values

$l=5.2$, $n=7$, $m\angle M=121^\circ$
$Area = \frac{1}{2}(5.2)(7)\sin(121^\circ) = 18.2 \times 0.8572 \approx 15.6$

Answer:

1. Rectangle
2. $60\pi \text{ cm}^2$
3. 15.6 square units