Mathematics: Which container has the greatest surface area? (use 3.14 for π.)

6 is the answer. Chile anyway so...

Which container has the greatest surface area? (use

matiasjjj14

18.01.2022

the last container, the rectangular solid, has the greatest surface area.

Step-by-step explanation:

Surface Area is the area of all the surfaces.

Figure 1 is a Cone. Surface Area of Cone is given by the formula $\pi r^2+\pi rl$

The slant height (l) is 10 and the radius is 3 (half of 6). Plugging in we get:

Surface Area = $\pi r^2+\pi rl=\pi (3)^2+\pi (3)(10)=122.46$

Figure 2 is a cylinder. Surface area of cylinder is given by the formula $2\pi r h + 2\pi r^2$

The radius is 3 and the height is 10. Pluggin in gives us:

Surface Area = $2\pi r h + 2\pi r^2=2\pi (3)(10)+2\pi (3)^2 = 244.92$

Figure 3 is a pyramid. This has 4 triangular faces each with length 6 and height 10 and one square with side 6.

Surface Area = $4(\frac{1}{2}bh)+s^2$

Plugging in the values, we get:

Surface Area = $4(\frac{1}{2}bh)+s^2 = 4(\frac{1}{2}(6)(10))+(6)^2=156$

Figure 4 is a rectangular solid with length 6, width 6 and height 10. The surface area is area of all the 6 surfaces. So we have:

Surface Area = 2(6*6)+2(6*10)+2(6*10)=312

Hence, the last container, the rectangular solid, has the greatest surface area.

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