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3 years ago

15

the volume of a sandbox shaped like a rectangular prism is 48 ft3. the height of the sandbox is 2 feet, the width is w feet and

the length is w + 2 feet. use the formula v= lwh to find the value of w

1 answer:

Effectus [21]3 years ago

3 0

Lwh=v
2*w*(w+2)=48
2w^2+4w=48
w^2+2w-24=0
(w+6)(w-4)=0
w= - 6 or w= 4
Since w cannot be negative, then w=4.

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Answer:

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Step-by-step explanation:

<u>GIVEN</u> :

As per given question we have provided that :

➣ Height of cylinder = 14 cm
➣ Curved surface area = 88 cm²

$\begin{gathered}\end{gathered}$

<u>TO</u><u> </u><u>FIND</u> :

in the provided question we need to find :

➠ Radius of cylinder
➠ Diameter of cylinder

$\begin{gathered}\end{gathered}$

<u>USING</u><u> </u><u>FORMULAS</u> :

$\star{\underline{\boxed{\sf{\purple{Csa = 2 \pi rh}}}}}$

$\star{\underline{\boxed{\sf{\purple{d = 2r}}}}}$

➛ Csa = Curved surface area
➛ π = 22/7
➛ r = radius
➛ h = height
➛ d = diameter

$\begin{gathered}\end{gathered}$

<u>SOLUTION</u> :

Firstly, finding the radius of cylinder by substituting the values in the formula :

$\begin{gathered} \qquad{\longrightarrow{\sf{Csa = 2 \pi rh}}} \\ \\ \qquad{\longrightarrow{\sf{88 = 2 \times \dfrac{22}{7} \times r \times 14}}} \\ \\ \qquad{\longrightarrow{\sf{88 =\dfrac{44}{7} \times r \times 14}}} \\ \\ \qquad{\longrightarrow{\sf{88 =\dfrac{44}{\cancel{7}}\times r \times \cancel{ 14}}}} \\ \\ \qquad{\longrightarrow{\sf{88 =44 \times r \times 2}}} \\ \\ \qquad{\longrightarrow{\sf{88 =88 \times r}}} \\ \\ \qquad{\longrightarrow{\sf{r = \frac{88}{88}}}} \\ \\ \qquad{\longrightarrow{\underline{\underline{\sf{\pink{r = 1 \: cm}}}}}} \end{gathered}$

Hence, the radius of cylinder is 1 cm.

———————————————————————

Now, finding the diameter of cylinder by substituting the values in the formula :

$\begin{gathered} \qquad{\longrightarrow{\sf{d = 2r}}} \\ \\ \qquad{\longrightarrow{\sf{d = 2 \times 1}}} \\ \\ \qquad{\longrightarrow{\underline{\underline{\sf{\red{r = 2 \: cm}}}}}}\end{gathered}$

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