raj, amit, parul, and lara were asked to find the volume of the following cones. raj amit parul lara 3 cm 4 cm 7 cm 6 cm 5 cm 3 cm b = 4π cm² b = 3π cm² whose cone has a volume closest to 9π cm³? lara parul raj amit

Question

Accepted Answer

# Explanation:
## Step1: Calculate Raj's cone volume
The formula for the volume of a cone is $V=\frac{1}{3}\pi r^{2}h$. For Raj, $r = 5$ cm and $h=3$ cm.
$$
\begin{align*}
V_{Raj}&=\frac{1}{3}\pi\times5^{2}\times3\
&=25\pi\space cm^{3}
\end{align*}
$$
## Step2: Calculate Amit's cone volume
For Amit, $r = 3$ cm and $h = 4$ cm.
$$
\begin{align*}
V_{Amit}&=\frac{1}{3}\pi\times3^{2}\times4\
&=12\pi\space cm^{3}
\end{align*}
$$
## Step3: Calculate Parul's cone volume
The formula for the volume of a cone is also $V=\frac{1}{3}Bh$ (where $B$ is the base area). For Parul, $B = 4\pi$ $cm^{2}$ and $h = 7$ cm.
$$
\begin{align*}
V_{Parul}&=\frac{1}{3}\times4\pi\times7\
&=\frac{28}{3}\pi\approx9.33\pi\space cm^{3}
\end{align*}
$$
## Step4: Calculate Lara's cone volume
For Lara, $B = 3\pi$ $cm^{2}$ and $h = 6$ cm.
$$
\begin{align*}
V_{Lara}&=\frac{1}{3}\times3\pi\times6\
&=6\pi\space cm^{3}
\end{align*}
$$

# Answer:
Parul

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Calculate Raj's cone volume

Step2: Calculate Amit's cone volume

Step3: Calculate Parul's cone volume

Step4: Calculate Lara's cone volume

Answer: