To find out how many pints of paint the skateboard club needs to purchase to paint the ramp, we first need to calculate the total surface area of the triangular prism.
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Calculate the area of the triangular face: The triangular face is a right triangle with a base of 8 inches and a height of 6 inches. The area of the triangle can be calculated using the formula: \[ \text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \times 6 = 24 \text{ square inches} \]
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Calculate the perimeter of the triangular face: The sides of the triangle are 8 inches (base), 6 inches (height), and 10 inches (hypotenuse). The perimeter is: \[ \text{Perimeter} = 8 + 6 + 10 = 24 \text{ inches} \]
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Calculate the surface area of the prism: The surface area (SA) of a triangular prism can be calculated as: \[ \text{SA} = 2 \times \text{Area}_{\text{triangle}} + \text{Perimeter} \times \text{length} \] Substituting the values we have: \[ \text{SA} = 2 \times 24 + 24 \times 19 \] Calculating each term: \[ 2 \times 24 = 48 \text{ square inches} \] \[ 24 \times 19 = 456 \text{ square inches} \] Therefore, \[ \text{SA} = 48 + 456 = 504 \text{ square inches} \]
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Calculate the number of pints of paint needed: Given that one pint of paint covers 200 square inches, we can determine the number of pints needed by dividing the total surface area by the coverage of one pint: \[ \text{Pints required} = \frac{504}{200} = 2.52 \] Since paint is sold in whole pints, we round up to the nearest whole number: \[ \text{Pints needed} = 3 \]
Thus, the skateboard club needs to purchase 3 pints of paint.