To solve this problem, we need to find the dimensions of the cuboid that minimize the surface area. The volume of a cuboid is given by the product of its length, width, and height (l*w*h), and the surface area is given by 2*(l*w + w*h + h*l).

Given that the volume is 2020 cm^3, we need to find the factors of 2020 that will minimize the surface area. The prime factorization of 2020 is 2*2*5*101.

To minimize the surface area, we should choose the dimensions to be as close together as possible. So, we choose 4 (2*2), 5, and 101 as the dimensions.

Then, the surface area is 2*(4*5 + 5*101 + 101*4) = 2*(20 + 505 + 404) = 2*929 = 1858 cm^2.

So, the smallest possible total surface area of the cuboid is 1858 cm^2.

Question

To solve this problem, we need to find the dimensions of the cuboid that minimize the surface area. The volume of a cuboid is given by the product of its length, width, and height (l*w*h), and the surface area is given by 2*(l*w + w*h + h*l).

Given that the volume is 2020 cm^3, we need to find the factors of 2020 that will minimize the surface area. The prime factorization of 2020 is 2*2*5*101.

To minimize the surface area, we should choose the dimensions to be as close together as possible. So, we choose 4 (2*2), 5, and 101 as the dimensions.

Then, the surface area is 2*(4*5 + 5*101 + 101*4) = 2*(20 + 505 + 404) = 2*929 = 1858 cm^2.

So, the smallest possible total surface area of the cuboid is 1858 cm^2.

Knowee AI · Accepted Answer

To solve this problem, we need to find the dimensions of the cuboid that minimize the surface area. The volume of a cuboid is given by the product of its length, width, and height (l*w*h), and the surface area is given by 2*(l*w + w*h + h*l).

Given that the volume is 2020 cm^3, we need to find the factors of 2020 that will minimize the surface area. The prime factorization of 2020 is 2*2*5*101.

To minimize the surface area, we should choose the dimensions to be as close together as possible. So, we choose 4 (2*2), 5, and 101 as the dimensions.

Then, the surface area is 2*(4*5 + 5*101 + 101*4) = 2*(20 + 505 + 404) = 2*929 = 1858 cm^2.

So, the smallest possible total surface area of the cuboid is 1858 cm^2.

A cuboid has a volume of 2020 cm3cm3 and the length of its sides are whole numbers of cm.cm. The length, breadth and height of this cuboid are such that the cuboid has the smallest possible total surface area. What is the total surface area of this cuboid?

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