Question

can you answer each question and type the correct code? please remember to type in all caps with no spaces. puzzle #5 answer choices a: b: c: 87.3 sphere 1436.4 d: e: f: 183.2 113.1 155.5 g: h: i: 179.6 cylinder 160.3 round to the nearest tenth type the 4 - letter code into the answer box. all caps, no spaces. 1 if the radius of the sphere is 3.5 meters, whats its volume, in m³? 2 whats the volume of the cylinder, in m³? 3 which shape has a greater volume? 4 which shape has a greater surface area?

Explanation:

Step1: Calculate sphere volume

The formula for the volume of a sphere is \(V_{sphere}=\frac{4}{3}\pi r^{3}\). Given \(r = 3.5\) meters, then \(V_{sphere}=\frac{4}{3}\times\pi\times(3.5)^{3}=\frac{4}{3}\times\pi\times42.875\approx179.6\) (matches option G).

Step2: Calculate cylinder volume

The formula for the volume of a cylinder is \(V_{cylinder}=\pi r^{2}h\). Given \(r = 3\) meters and \(h=5.5\) meters, then \(V_{cylinder}=\pi\times3^{2}\times5.5=\pi\times9\times5.5 = 155.5\) (matches option F).

Step3: Compare volumes

Since \(179.6>155.5\), the sphere (option B) has a greater volume.

Step4: Calculate sphere surface area

The formula for the surface area of a sphere is \(A_{sphere}=4\pi r^{2}\). With \(r = 3.5\), \(A_{sphere}=4\times\pi\times(3.5)^{2}=4\times\pi\times12.25\approx153.9\).

Step5: Calculate cylinder surface area

The formula for the surface area of a cylinder is \(A_{cylinder}=2\pi r(r + h)\). With \(r = 3\) and \(h = 5.5\), \(A_{cylinder}=2\times\pi\times3\times(3 + 5.5)=6\pi\times8.5\approx160.2\) (matches option I).

Answer:

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