Question
1. At closed cylinder has radios 3 cm and height 7 cm . Find its tatal surface area
Ask by Kirk Stewart. in Ghana
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The total surface area of the closed cylinder is approximately 188.5 cm².
Solution
To find the total surface area of a closed cylinder, we need to calculate the area of the two circular bases and the area of the curved surface.
Given:
- Radius of the cylinder = 3 cm
- Height of the cylinder = 7 cm
The formula for the total surface area of a closed cylinder is:
\[ \text{Total Surface Area} = 2 \pi r^2 + 2 \pi r h \]
Where:
- \( r \) is the radius of the cylinder
- \( h \) is the height of the cylinder
Substitute the given values into the formula:
\[ \text{Total Surface Area} = 2 \pi (3)^2 + 2 \pi (3) (7) \]
Now, we can calculate the total surface area.
Calculate the value by following steps:
- step0: Calculate:
\(2\pi \times 3^{2}+2\pi \times 3\times 7\)
- step1: Multiply the terms:
\(18\pi +2\pi \times 3\times 7\)
- step2: Multiply the terms:
\(18\pi +42\pi \)
- step3: Collect like terms:
\(\left(18+42\right)\pi \)
- step4: Add the numbers:
\(60\pi \)
The total surface area of the closed cylinder is approximately 188.5 cm².
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To find the total surface area of a closed cylinder, we can use the formula: Total Surface Area = 2πr(h + r), where r is the radius and h is the height. Substituting the given values, we have r = 3 cm and h = 7 cm. Therefore, the total surface area is 2π(3)(7 + 3) = 2π(3)(10) = 60π cm², which is approximately 188.5 cm² when calculated. Now, remember to keep your units consistent! Using centimeters for both the radius and height is crucial for obtaining the correct measurement of surface area. A little oversight here, like using different units, can lead to a significantly incorrect total surface area calculation!
