Question

Math question please show work due today last day to submit Assignments or I fail please help

Answer 1

`\text{a. }123.2\:\mathrm{cm^2},\\\text{b. }136\:\mathrm{m^2}`

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
`A=r^2\pi`, where
`r` 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:
`2\cdot 2^2\pi=8\pi=25.1327412287`

Area of side:
`7.8\cdot 2\cdot 2\cdot \pi=31.2\pi=98.017690792`

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

Part A:

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

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

Answer 2

9514 1404 393

Answer:

a. 123.2 cm²

b. 136 m²

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

_____

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.