Pregunta
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2. John wants to cover the top and bottom of a soup can with paper. Which portion o the surface area formula, \( S A=2 \pi r^{2}+2 \pi r h \), can John use to find the area of th top and bottom of the can? \( 2 \pi r h \) \( r h \) \( 2 \pi r^{2} \) \( \pi r^{2} \)

Ask by Edwards Christensen. in the United States
Jan 23,2025

Solución de tutoría real

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John should use \(2 \pi r^{2}\) to find the area of the top and bottom of the can.

Solución

To find the area of the top and bottom of a soup can, we need to focus on the portion of the surface area formula that corresponds to these two circular areas. The surface area formula for a cylinder is given by: \[ SA = 2 \pi r^{2} + 2 \pi r h \] Where: - \(2 \pi r^{2}\) represents the area of the top and bottom circles (two circles). - \(2 \pi r h\) represents the lateral surface area of the cylinder. Since John wants to cover only the top and bottom of the can, he should use the portion of the formula that corresponds to the area of the circles. The area of one circle is given by: \[ \pi r^{2} \] Since there are two circles (top and bottom), the total area for both is: \[ 2 \pi r^{2} \] Thus, the correct portion of the surface area formula that John can use to find the area of the top and bottom of the can is: \[ \boxed{2 \pi r^{2}} \]

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Mind Expander

To cover the top and bottom of the soup can, John should focus on the area of the circles formed by the top and bottom. This area is calculated using the formula for the area of a circle, which is \( \pi r^2 \). Since there are two circles (top and bottom), he must multiply this by 2, leading to the expression \( 2 \pi r^{2} \). In practice, this means John will need to measure the radius of the can to effectively determine how much paper he will need. By using the formula \( 2 \pi r^{2} \), he can quickly calculate the total area he needs to cover without overestimating or wasting material. Happy crafting, John!

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