Question

Please help if you can, thank you! it means a lot <3

Answer 1

Answer :

$\huge\frak{\underline{\red{Number\:of\:boxes\: = 54}}}$

Explanation :

In attachment.

Answer 2

$\huge\bf\underline\mathfrak{Answer :}$

$\text{Number of boxes that can be fit into this truck}$ = $\text\purple {54 boxes}$

$\huge\bf\underline\mathfrak{Step \: by \: step \: explanation :}$

$\huge\bf\underline\mathfrak{Given :}$

• $\text{Length of the truck}$ = $\sf\red{15 \: feet.}$
• $\text{Breadth of the truck}$ = $\sf\red{7.5 \: feet.}$
• $\text{Height of the truck}$ = $\sf\red{7.5 \: feet.}$
• $\text{Side of the boxes}$ = $\sf\blue{2.5 \: feet.}$

$\huge\bf\underline\mathfrak{To \: find :}$

• $\text{Number of boxes fitted in the truck.}$

$\huge\bf\underline\mathfrak{Concept :}$

• Here, we're given a cuboidal truck and cubical boxes. Along with that, dimensions of both the sides are also given. We're asked to find out how many boxes can be fitted into that truck.

• Since, number of boxes is asked, we're supposed to calculate the volume of both the figures.

• After calculating the volume, we'll find the number of boxes with a relation between volume of cuboidal truck and the cubical box.

$\huge\bf\underline\mathfrak{Solution :}$

$\sf\underbrace{Volume \: of \: truck :-}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀$\text{Volume}$ = $\sf\red{l × b × h}$⠀⠀⠀⠀⠀⠀⠀⠀⠀

• Where,

1. l = length of the truck.
2. b = breadth of the truck.
3. h = height of the truck.

$\underline\text{Substituting the given values in the formula :-}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀$\sf{Volume}$ = $\sf\red{(15 × 7.5 × 7.5) cm³}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\implies$ $\sf\red{843.75 \: cm³}$

$\sf\underbrace{Volume \: of \: Cubical \: box :-}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀$\text{Volume}$ = $\sf\purple{a³}$

• Where, a = side of the cubical box.

$\underline\text{Substituting the given values in the formula :-}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀$\sf{Volume}$ = $\sf\purple{(2.5)³ cm³}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\implies$ $\sf\purple{15.625 \: cm³}$

$\sf\underbrace{Calculating \: number \: of \: boxes :-}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀$\sf boxes \: = \dfrac\red{Volume \: of \: truck}\purple{Volume \: of \: 1 \: box}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\implies$ $\sf \dfrac{843.75}{15.625}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\implies$ $\sf\green{54 \: boxes}$

Hence,

• Number of boxes = 54.

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