Question

1. calculate the surface areas of the following composite 3 - d objects. round to the nearest whole number.

a. r = 7.2 cm 16.0 cm

Explanation:

Step1: Identify component - shapes

The composite 3 - D object can be seen as two semi - circles (which together form a full circle) and a rectangle with curved ends. The formula for the area of a circle is $A_{circle}=\pi r^{2}$ and for the lateral area of the cylindrical - part (rectangle with curved ends) is $A_{lateral}=2\pi r h$, where $h$ is the length of the straight part of the object.

Step2: Calculate the area of the circle

Given $r = 7.2$ cm, $A_{circle}=\pi r^{2}=\pi\times(7.2)^{2}=\pi\times51.84\approx3.14\times51.84 = 162.7776$ $cm^{2}$.

Step3: Calculate the lateral area

The length of the straight part of the object is $l = 16.0$ cm. The lateral area $A_{lateral}=2\pi rl$. Substituting $r = 7.2$ cm and $l = 16.0$ cm, we get $A_{lateral}=2\times3.14\times7.2\times16.0=2\times3.14\times115.2 = 723.456$ $cm^{2}$.

Step4: Calculate the total surface area

The total surface area $A = A_{circle}+A_{lateral}=162.7776 + 723.456=886.2336\approx886$ $cm^{2}$.

Answer:

$886$ $cm^{2}$