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Zorluk: OrtaVolume and Surface Area of 3D Figures

A community center is repainting the inside of an empty rectangular swimming pool. The pool is 2525 meters long, 1010 meters wide, and has a uniform depth of 22 meters. If the entire bottom and all four interior walls are to be painted, what is the total area, in square meters, that needs to be painted?

Cevap: 390 square meters

Cevap

390
The correct total area is found by adding the area of the bottom (250250 m 2^2) and the areas of the four vertical walls (100100 m 2^2 and 4040 m 2^2). Because it is a swimming pool, there is no top to paint, making the total area 390390 square meters.

Adım Adım Çözüm

1
Determine which surfaces of the rectangular pool need to be painted.
One bottom surface and four side walls (two long and two short). The top is open.
A pool is shaped like an open-top rectangular prism, so we only need to calculate the area of 5 faces instead of 6.
2
Calculate the area of the bottom surface.
Area = 25×10=25025 \times 10 = 250 square meters.
The bottom is a rectangle bounded by the length and width of the pool.
3
Calculate the combined area of the four side walls.
Long walls = 2×(25×2)=1002 \times (25 \times 2) = 100 square meters. Short walls = 2×(10×2)=402 \times (10 \times 2) = 40 square meters.
There are two identical walls along the length and two identical walls along the width. The area of each wall is its base dimension multiplied by the depth.
4
Sum the areas of all the painted surfaces.
250+100+40=390250 + 100 + 40 = 390 square meters.
The total area to be painted is the sum of the areas of the individual painted faces.

Anahtar Kavram

Surface area of an open rectangular prism
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Konular

Volume and Surface Area of 3D Figures

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