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3 years ago

NEED ANSWER ASAP- FOR FINALS

Mathematics

1 answer:

puteri [66]3 years ago

4 0

Answer:

The smaller dimension of the pool is 14 ft.

The larger dimension of the pool is 35 ft.

Step-by-step explanation:

We are told that:

The rectangular swimming pool is 6 ft deep. Thus, depth: h = 6 ft

One side of the pool is 2.5 times longer than the other.

Thus, length = 2.5(width)

l = 2.5w and width = w

Volume; V = lwh = (2.5w × w × 6) = 15w²

The amount of water needed to fill the swimming pool is 2940 cubic feet.

Thus;

15w² = 2940

w² = 2940/15

w² = 196

w = √196

w = 14 ft

Length: L = 2.5w = 2.5 × 14 = 35 ft

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the trunk is really just a half-cylinder on top of a square, with a depth of 2 meters

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take the volume of the rectangular prism, and then add them both

$\bf \textit{volume of a cylinder}\\\\

\begin{array}{llll}
C=\pi r^2 h\\\\
\textit{half that}\\\\
\cfrac{\pi r^2 h}{2}
\end{array}\qquad 
\begin{cases}
r=radius\\
h=height\\
-------\\
r=\frac{1}{2}\\
h=2
\end{cases}\implies \cfrac{C}{2}=\cfrac{\pi \left( \frac{1}{2}\right)^2 2}{2}\\\\
-----------------------------\\\\
\textit{volume of a square}\\\\
V=lwh\qquad 
\begin{cases}
l=length\\
w=width\\
h=height
----------\\
l=1\\
w=1\\
h=2
\end{cases}\implies V=2$

now.. for the surface area... $\bf \textit{surface area of a cylinder}\\\\
\begin{array}{llll}
S=2\pi r(h+r)\\\\
\textit{half that}\\\\
\cfrac{2\pi r(h+r)}{2}
\end{array}\begin{cases}
r=radius\\
h=height\\
-------\\
r=\frac{1}{2}\\
h=2
\end{cases}$

now.. for the surface area of the prism... well

is really just 6 rectangles stacked up to each other at the edges

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for the lateral ones, you have a front of 1x1, a back of 1x1 and a left of 1x2 and a right of 1x2, and then the one at the bottom, which is a 1x2

then add both surface areas, and that's the surface area of the trunk

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