Question

Which container has the greatest surface area? (Use 3.14 for π.)

Answer 1

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

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((1)/(2)bh)+s^2`

Plugging in the values, we get:

Surface Area =
`4((1)/(2)bh)+s^2 = 4((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.