determine the volume and the surface area of the three - dimensional figure. use the π key on your calculator.
a) the volume is
(simplify your answer. type an integer or a decimal rounded to the nearest hundredth as needed.)
b) the surface area is
(simplify your answer. type an integer or a decimal rounded to the nearest hundredth as needed.)

Question

determine the volume and the surface area of the three - dimensional figure. use the π key on your calculator.
 a) the volume is
 (simplify your answer. type an integer or a decimal rounded to the nearest hundredth as needed.)
 b) the surface area is
 (simplify your answer. type an integer or a decimal rounded to the nearest hundredth as needed.)

Accepted Answer

# Explanation:
## Step1: Calculate the volume of the cone
The formula for the volume of a cone is $V=\frac{1}{3}\pi r^{2}h$. Given $r = 3$ cm and $h=7$ cm.
$$
\begin{align*}
V&=\frac{1}{3}\times\pi\times3^{2}\times7\
&=\frac{1}{3}\times\pi\times9\times7\
& = 21\pi\
&\approx21\times3.14\
&=65.94\space\text{cm}^{3}
\end{align*}
$$
## Step2: Calculate the slant height $l$ of the cone
Use the Pythagorean theorem $l=\sqrt{r^{2}+h^{2}}$. Substitute $r = 3$ cm and $h = 7$ cm.
$$
\begin{align*}
l&=\sqrt{3^{2}+7^{2}}\
&=\sqrt{9 + 49}\
&=\sqrt{58}\approx7.62\space\text{cm}
\end{align*}
$$
## Step3: Calculate the surface area of the cone
The formula for the surface area of a cone is $A=\pi r(r + l)$. Substitute $r = 3$ cm and $l\approx7.62$ cm.
$$
\begin{align*}
A&=\pi\times3\times(3 + 7.62)\
&=3\pi\times10.62\
&\approx3\times3.14\times10.62\
&=9.42\times10.62\
&=100.0\space\text{cm}^{2}
\end{align*}
$$

# Answer:
a) The volume is $65.94\space\text{cm}^{3}$
b) The surface area is $100.0\space\text{cm}^{2}$

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the volume of the cone

Step2: Calculate the slant height \(l\) of the cone

Step3: Calculate the surface area of the cone

Answer: