QuestionJuly 15, 2025

Find the surface area of a cone with a radius of 2.9'' and a height of 19''. Click Here Add your answer

Find the surface area of a cone with a radius of 2.9'' and a height of 19''. Click Here Add your answer
Find the surface area of a cone with a radius of 2.9'' and a height of 19''. Click Here Add your answer

Solution
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Answer

The total surface area is approximately 196.57 \text{ square inches}. Explanation 1. Calculate the slant height Use the Pythagorean theorem: l = \sqrt{r^2 + h^2}. Here, r = 2.9 and h = 19. So, l = \sqrt{(2.9)^2 + (19)^2}. 2. Calculate the lateral surface area Use the formula for lateral surface area: A_{\text{lateral}} = \pi r l. Substitute r = 2.9 and calculated l. 3. Calculate the base area Use the formula for the area of a circle: A_{\text{base}} = \pi r^2. Substitute r = 2.9. 4. Calculate the total surface area Add the lateral surface area and the base area: A_{\text{total}} = A_{\text{lateral}} + A_{\text{base}}.

Explanation

1. Calculate the slant height<br /> Use the Pythagorean theorem: $l = \sqrt{r^2 + h^2}$. Here, $r = 2.9$ and $h = 19$. So, $l = \sqrt{(2.9)^2 + (19)^2}$.<br />2. Calculate the lateral surface area<br /> Use the formula for lateral surface area: $A_{\text{lateral}} = \pi r l$. Substitute $r = 2.9$ and calculated $l$.<br />3. Calculate the base area<br /> Use the formula for the area of a circle: $A_{\text{base}} = \pi r^2$. Substitute $r = 2.9$.<br />4. Calculate the total surface area<br /> Add the lateral surface area and the base area: $A_{\text{total}} = A_{\text{lateral}} + A_{\text{base}}$.
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