Question

type in all caps with no spaces.
puzzle #4
answer choices
a: cone b: 268.1 c: sphere
d: 282.7 e: 254.5 f: 1017.5
g: 942.5 h: 2262.4 i: 84.8
round to the nearest tenth
diameter = 9 inches
height = 12 in
r = 5 inches
1 whats the surface area of the sphere, in square inches?
2 whats the surface area of the cone, in in²?
3 which shape has a greater surface area?
4 which shape has a greater volume?
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your answer
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Explanation:

Step1: Surface area of sphere

The formula for the surface area of a sphere is \(S = 4\pi r^{2}\). Given \(d = 9\) inches, then \(r=\frac{d}{2}=\frac{9}{2}=4.5\) inches. Substitute \(r = 4.5\) into the formula: \(S=4\pi(4.5)^{2}=4\pi\times20.25 = 81\pi\approx81\times3.14 = 254.34\approx254.5\) (E).

Step2: Surface area of cone

The formula for the surface area of a cone is \(S=\pi r(r + l)\), where \(l=\sqrt{r^{2}+h^{2}}\). Given \(r = 5\) inches and \(h = 12\) inches, then \(l=\sqrt{5^{2}+12^{2}}=\sqrt{25 + 144}=\sqrt{169}=13\) inches. Substitute \(r = 5\) and \(l = 13\) into the formula: \(S=\pi\times5\times(5 + 13)=5\pi\times18=90\pi\approx90\times3.14 = 282.6\approx282.7\) (D).

Step3: Compare surface areas

Since \(282.7>254.5\), the cone (A) has a greater surface area.

Step4: Volume of sphere and cone

The volume of a sphere \(V_{s}=\frac{4}{3}\pi r^{3}\), with \(r = 4.5\), \(V_{s}=\frac{4}{3}\pi(4.5)^{3}=\frac{4}{3}\pi\times91.125=121.5\pi\approx121.5\times3.14 = 381.51\). The volume of a cone \(V_{c}=\frac{1}{3}\pi r^{2}h\), with \(r = 5\) and \(h = 12\), \(V_{c}=\frac{1}{3}\pi\times5^{2}\times12=\frac{1}{3}\pi\times300 = 100\pi\approx314\). So the sphere (C) has a greater volume.

Answer:

EDAC