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mel-nik [20]
2 years ago
14

NO LINKS!!!! Find the Lateral Area, Total Surface Area, and Volume. Round your answer to two decimal places.​

Mathematics
2 answers:
g100num [7]2 years ago
8 0

Answer:

<u>Lateral Surface Area</u>: The total surface area of a three-dimensional object, excluding the bases.

<h3><u>Question 5</u></h3>

Figure:  <u>Rectangular prism</u>

Given:

  • length (l) = 10 m
  • width (w) = 4 m
  • height (h) = 6 m

<u>Lateral Surface Area</u>

\begin{aligned}\textsf{L.A. of a rectangular prism} & = 2h(l+w)\\\implies \sf L.A. & = \sf 2 \cdot 6(10+4)\\& = \sf 168\:\:m^2\end{aligned}

<u>Total Surface Area</u>

\begin{aligned}\textsf{T.A. of a rectangular prism} & = 2(lw+lh+wh)\\\implies \sf T.A. & = 2(10 \cdot 4+10 \cdot 6+4 \cdot 6)\\& = 248\:\: \sf m^2\end{aligned}

<u>Volume</u>

\begin{aligned}\textsf{Volume of a rectangular prism} & = whl\\\implies \sf T.A. & = 4 \cdot 6 \cdot 10\\& = 240\:\: \sf m^3\end{aligned}

<h3><u>Question 6</u></h3>

Figure: <u>Triangular Prism</u>

The <u>bases</u> of a triangular prism are the <u>triangles.</u>

<u />

First, find the hypotenuse of the right triangular base using Pythagoras' Theorem a^2+b^2=c^2  where a and b are the legs and c is the hypotenuse.

\implies 5^2+8^2=c^2

\implies c^2=89

\implies c=\sqrt{89}

<u>Lateral Surface Area</u>

The L.A. is made up of 3 rectangles, each with a length of 12 ft and a width of one side of the triangular base.

\begin{aligned}\implies \sf L.A. & = \sf 12(8+5+\sqrt{89})\\& = \sf 269.21\:\:ft^2\end{aligned}

<u>Total Surface Area</u>

The T.A. is made up of the L.A. plus the areas of the triangular bases.

\begin{aligned}\textsf{Area of a triangle} & = \dfrac{1}{2}bh\\\implies \sf A & = \dfrac{1}{2} \cdot 8 \cdot 5\\& = 20\:\: \sf ft^2\end{aligned}

\begin{aligned}\implies \sf T.A. & = \sf L.A.+2\:base\:areas\\ & = 269.21+2(20)\\& = 309.21\:\: \sf ft^2\:(2\:d.p.)\end{aligned}

<u>Volume</u>

\begin{aligned}\textsf{Volume of a triangular prism} & = \sf base\:area \times height\\\implies \sf Vol. & = 20 \cdot 12\\& = 240\:\: \sf ft^3\end{aligned}

valina [46]2 years ago
3 0

#1

  • l=6
  • b=4
  • h=10

LsA

  • 2×h(l+b)
  • 2(10)(6+4)
  • 200.00m²

TSA

  • 2(lb+bh+lh)
  • 2(6×4+4×10+10×6)
  • 2(24+40+60)
  • 248.00m²

Volume.

  • lbh
  • 10(6)(4)
  • 240m³

#2

  • l=5ft
  • b=8ft

LSA

  • 3lb
  • 2(5)(8)
  • 120ft²

TSA

Hypotenuse=√5²+8²=√89=9.4

  • 5(8)+9.4(12)+12(8)+5(12)
  • 40+112.8+96+60
  • 308.8ft²

Volume

  • Area of base×Height
  • 1/2(5)(8)(12)
  • 20(12)
  • 240ft³
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