Question Video: Identifying the System with the Highest Total Surface Area Value | Nagwa Question Video: Identifying the System with the Highest Total Surface Area Value | Nagwa

Question Video: Identifying the System with the Highest Total Surface Area Value Chemistry • Third Year of Secondary School

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The combinations of shapes all have the same total volume. Which has the greatest total surface area?

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Video Transcript

The following combinations of shapes all have the same total volume. Which has the greatest total surface area?

In chemistry, the surface area of reactants impacts the rate of reaction. We can compare the same amount of reactant in two different forms: one where the reactant is in a large piece, so the amount of particles on the surface is relatively small. In the other, the reactant is ground up, perhaps into a fine powder, which increases the amount of particles exposed to the surface. The reactant in one piece will have a slower rate of reaction because only the particles on the surface can immediately react. When the reactant is ground up into smaller pieces, more particles are available to react.

Based on these pictures, we can guess that answer choice (B) will have the greatest surface area because there is the greatest number of shapes. But we can do some math to confirm our answer. Let’s start off by calculating the surface area of this cube. The cube has sides of 10 centimeters. So one face of the cube has an area of 100 centimeters squared. A cube has six faces. So the total surface area will be six times the area of one face. That gives us 600 centimeters squared.

Answer choice (C) has two shapes instead of one. Let’s see if we can figure out the pattern here by calculating the surface area for these shapes. There are two different size faces in the shape. One size face has sides of 10 centimeters and 10 centimeters. The area of these faces is 100 centimeters squared. The other faces have sides of five centimeters and 10 centimeters. So these faces have an area of 50 centimeters squared.

Now let’s calculate the total surface area for these shapes. Each shape has two faces that have an area of 100 centimeters squared. And each shape has four faces that have an area of 50 centimeters squared. So the surface area of one of the shapes is 400 centimeters squared. There are two of these shapes. So we need to multiply the surface area we just calculated by two to get the total surface area for both of the shapes. This means the total surface area for the two shapes is 800 centimeters squared.

If we were to calculate the surface area of the remaining shapes, we would find that the surface area for the eight cubes in answer choice (B) is 1200 centimeters squared. The total surface area for the shapes in answer choice (D) is 1000 centimeters squared. So we can see the trend here is that the surface area increases when there is a larger number of shapes.

So we’ve confirmed our answer. The combination of shapes that has the greatest total surface area is the one with the greatest number of shapes, which is the eight cubes shown in answer choice (B).

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