puzzle #5
answer choices
a: 87.3 b: sphere c: 1436.4
d: 183.2 e: 113.1 f: 155.5
g: 179.6 h: cylinder i: 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?

Question

Accepted Answer

# Explanation:
## Step1: Calculate the volume of the sphere
The formula for the volume of a sphere is $V_{sphere}=\frac{4}{3}\pi r^{3}$. Given $r = 3.5$ meters.
$$
\begin{align*}
V_{sphere}&=\frac{4}{3}\times\pi\times(3.5)^{3}\
&=\frac{4}{3}\times\pi\times42.875\
&\approx179.6\space m^{3}
\end{align*}
$$
## Step2: Calculate the volume of the cylinder
The formula for the volume of a cylinder is $V_{cylinder}=\pi r^{2}h$. Given $r = 3$ meters and $h=5.5$ meters.
$$
\begin{align*}
V_{cylinder}&=\pi\times(3)^{2}\times5.5\
&=\pi\times9\times5.5\
&= 155.5\space m^{3}
\end{align*}
$$
## Step3: Compare the volumes
Since $179.6>155.5$, the sphere ($B$) has a greater volume.
## Step4: Calculate the surface area of the sphere
The formula for the surface area of a sphere is $A_{sphere} = 4\pi r^{2}$. For $r = 3.5$
$$
\begin{align*}
A_{sphere}&=4\times\pi\times(3.5)^{2}\
&=4\times\pi\times12.25\
&=153.9\space m^{2}
\end{align*}
$$
## Step5: Calculate the surface area of the cylinder
The formula for the surface area of a cylinder is $A_{cylinder}=2\pi r(r + h)$. For $r = 3$ and $h = 5.5$
$$
\begin{align*}
A_{cylinder}&=2\times\pi\times3\times(3 + 5.5)\
&=6\pi\times8.5\
&=160.2\space m^{2}
\end{align*}
$$
Since $160.2>153.9$, the cylinder ($H$) has a greater surface area.

# Answer:
GHC I

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the volume of the sphere

Step2: Calculate the volume of the cylinder

Step3: Compare the volumes

Step4: Calculate the surface area of the sphere

Step5: Calculate the surface area of the cylinder

Answer: