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sqdancefan

9514 1404 393

Answer:

  a. 123.2 cm²

  b. 136 m²

Step-by-step explanation:

Use the formulas.

a) The formula is ...

  SA = 2πr(r+h) . . . . where r is half the diameter, and h is the height.

  SA = 2π(2 cm)(2 cm +7.8 cm) = 2·2·9.8π cm² = 123.2 cm²

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b) The formula is ...

  SA = 2(LW +H(L+W))

  SA = 2((8 m)(3 m) +(4 m)(8 m +3 m)) = 2(24 m² +44 m²) = 136 m²

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For the cylinder, we used the "pi button" and rounded to tenths. If you use 3.14 for π, you get 123.1 cm² when rounded to tenths.

Corsaquix

Answer:

[tex]\text{a. }123.2\:\mathrm{cm^2},\\\text{b. }136\:\mathrm{m^2}[/tex]

Step-by-step explanation:

Part A:

The total surface area of the cylinder consists of two circular bases and a side area. The area of a circle is given by [tex]A=r^2\pi[/tex], where [tex]r[/tex] is the radius of the circle. Since the diameter is given as 4 cm, the radius must be 2 cm.

Area of two circular bases: [tex]2\cdot 2^2\pi=8\pi=25.1327412287[/tex]

Area of side: [tex]7.8\cdot 2\cdot 2\cdot \pi=31.2\pi=98.017690792[/tex]

Therefore, the cylinder's total surface area is [tex]25.1327412287+98.017690792=123.150432021\approx \boxed{123.2\:\mathrm{cm^2}}[/tex]

Part A:

The total surface area of a rectangular prism with width [tex]w[/tex], length [tex]l[/tex], and height [tex]h[/tex] is given by [tex]2(hl+hw+lw)[/tex].

Thus, the total surface area of the rectangular prism is [tex]2(4\cdot 8+4\cdot 3+8\cdot 3)=2(32+12+24)=2(68)=\boxed{136\:\mathrm{m^2}}[/tex]

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