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3 years ago

14

Given a soda can with a volume of 15 and a diameter of 2, what is the volume of a cone that fits perfectly inside the soda can?

1 answer:

Naddika [18.5K]3 years ago

8 0

Check the picture below.

so, a cone, that fits inside the cylinder, will have the same height "h" and radius "r". Thus

$\bf \textit{volume of a cylinder}\\\\
V=\pi r^2 h\qquad \boxed{\pi r^2 h}=15
\\\\\\
\textit{volume of a cone}\\\\
V=\cfrac{\pi r^2 h}{3}\implies V=\cfrac{\boxed{15}}{3}$

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Jet001 [13]

Answer:

Therefore the rate of growth of the tree is 33 cm/ yr.

Step-by-step explanation:

Given that,

The height of the tree is

H= 210 +33t

Here H represent the height of tree in cm and t is time in year.

The rate of growth is the first order derivative of the H with respect to time.

i.e The rate of growth $=\frac{dH}{dt}$

∴H= 210 +33t

Differentiating with respect to t

$\frac{dH}{dt} =0 +33$

$\Rightarrow \frac{dH}{dt}=33$

Therefore the rate of growth of the tree is 33 cm/ yr.

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NNADVOKAT [17]

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4 years ago

I'LL GIVE YOU BRAINIEST!<br> 1 1/5 · x/3 = 9/10 solve for x

joja [24]

$\huge\text{Hey there!}$

$\huge\textbf{Equation:}$

$\mathbf{1 \dfrac{1}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}$

$\huge\textbf{Solve:}$

$\mathbf{1 \dfrac{1}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}$

$\mathbf{\rightarrow \dfrac{1\times5+1}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}$

$\mathbf{\rightarrow \dfrac{5 + 1}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}$

$\mathbf{\rightarrow \dfrac{6}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}$

$\huge\textbf{Simplify it:}$

$\mathbf{\rightarrow \dfrac{2}{5}x = \dfrac{9}{10}}$

$\huge\textbf{Multiply \boxed{\bf \dfrac{5}{2}} to both sides:}$

$\mathbf{\rightarrow \dfrac{5}{2}\times \dfrac{2}{5}x = \dfrac{5}{2}\times \dfrac{9}{10}}$

$\huge\textbf{Simplify it:}$

$\mathbf{\rightarrow x = \dfrac{5}{2}\times \dfrac{9}{10}}$

$\mathbf{\rightarrow x = \dfrac{5\times9}{2\times10}}$

$\mathbf{\rightarrow x = \dfrac{45}{20}}$

$\mathbf{\rightarrow x = \dfrac{45\div5}{20\div5}}$

$\mathbf{\rightarrow x = \dfrac{9}{4}}$

$\mathbf{x \approx 2 \dfrac{1}{4}}$

$\huge\textbf{Therefore, your answer should be:}$

$\huge\boxed{\mathsf{x = }\frak{2 \dfrac{1}{4}}}\huge\checkmark$

$\huge\text{Good luck on your assignment \& enjoy your day!}$

~ $\frak{Amphitrite1040:)}$

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