Answer:
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 [tex]\pi r^2+\pi rl[/tex]
The slant height (l) is 10 and the radius is 3 (half of 6). Plugging in we get:
Surface Area = [tex]\pi r^2+\pi rl=\pi (3)^2+\pi (3)(10)=122.46[/tex]
Figure 2 is a cylinder. Surface area of cylinder is given by the formula [tex]2\pi r h + 2\pi r^2[/tex]
The radius is 3 and the height is 10. Pluggin in gives us:
Surface Area = [tex]2\pi r h + 2\pi r^2=2\pi (3)(10)+2\pi (3)^2 = 244.92[/tex]
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 = [tex]4(\frac{1}{2}bh)+s^2[/tex]
Plugging in the values, we get:
Surface Area = [tex]4(\frac{1}{2}bh)+s^2 = 4(\frac{1}{2}(6)(10))+(6)^2=156[/tex]
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 = [tex]2(6*6)+2(6*10)+2(6*10)=312[/tex]
Hence, the last container, the rectangular solid, has the greatest surface area.
