thegreenappledragon thegreenappledragon

22-05-2022
Mathematics

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help with applications of surface area and volume problems! will reward brainly, 10th grade geometry

help with applications of surface area and volume problems will reward brainly 10th grade geometry class=

help with applications of surface area and volume problems will reward brainly 10th grade geometry class=

Respuesta :

Hrishii Hrishii

22-05-2022

Answer:

Question 1:

Rectangular prism requires [tex] 10.185\: in^2[/tex] more material to make than the cylinder.

Question 4:

The cylindrical container holds [tex]\bold{60.16\: in^3}[/tex] more than the rectangular prism.

Step-by-step explanation:

Question 1:

In order to select the correct answer, we should find the surface areas (SA) of both cylindrical as well as rectangular containers. Let us start...
For cylindrical container:
h = 10 in & r = 4.5 in

[tex] SA (Cylindrical \:container) = 2\pi rh+2\pi r^2-\pi r^2[/tex] ([tex]\pi r^2[/tex] is subtracted because the container is open from the top)

[tex] SA (Cylindrical \:container) = 2\pi rh+\pi r^2[/tex]

[tex] SA (Cylindrical \:container) = 2(3.14)(4.5)(10)+3.14 (4.5)^2[/tex]

[tex]\implies \red{\boxed{\bold{SA (Cylindrical \:container) =346.185\: in^2}}}[/tex]

Next, we find the surface area of the rectangular container which has following dimensions.
[tex] l = 8\: in,\: b = 8\: in,\: h= 8.5\: in[/tex]

[tex] SA ( rectangular\: container) = 2(lb+bh+lh)-lb[/tex] (lb is subtracted because container is open from the top)

[tex] \implies SA ( rectangular\: container) = lb+2(bh+lh)[/tex]

[tex] \implies SA ( rectangular\: container) = 8*8+2(8*8.5+8*8.5)[/tex]

[tex] \implies \purple{\boxed{\bold{SA ( rectangular\: container) = 336\: in^2}}}[/tex]

Here, SA (Cylindrical container) > SA (rectangular container)

[tex] Difference = 346.185 - 336 = 10.185\: in^2[/tex]

[tex]\bigodot[/tex] This means: rectangular prism requires [tex]\bold{10.185\: in^2}[/tex] more material to make than the cylinder.

Question 4:

[tex] V_{Cylinderical\: container}= \pi r^2 h [/tex]

[tex] \implies V_{Cylinderical\: container} =3.14 (4)^2 (9)[/tex]

[tex]\implies\red{\boxed{\bold{V_{Cylindrical\: container}=452.16\: in^3}}}[/tex]

[tex]V_{rectangular\: container}= l*b* h[/tex]

[tex] \implies V_{rectangular\: container}= 7*7* 8[/tex]

[tex] \implies \orange{\boxed{\bold{V_{rectangular\: container}= 392\: in^3}}}[/tex]

Here, [tex] V_{Cylinder\: container}>V_{rectangular\: container}[/tex]
[tex] Difference = 452.16 - 392= 60.16\: in^3[/tex]

[tex]\bigodot[/tex] Thus, the cylindrical container holds [tex]\bold{60.16\: in^3}[/tex] more than the rectangular prism.

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