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A copper pipe has the dimensions shown in the figure below. Calculate both the Total Surface area and the Volume of the copper in pipe in Cubic Metres.

Mathematics

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Kutokana na mchoro, bomba linaonyeshwa kama silinda yenye mashimo, lakini kipenyo cha ndani au unene wa ukuta haujatolewa. Kwa hivyo, tutachukulia bomba kama silinda imara (solid cylinder) kwa mahesabu haya, tukitumia vipimo vilivyotolewa.

Vipimo vilivyotolewa:
Urefu wa bomba (hh) = 2.5 M2.5 \text{ M}
Kipenyo cha nje (DD) = 25 cm25 \text{ cm}

  1. Badilisha vipimo vyote kuwa mita.

    Urefu h=2.5 mh = 2.5 \text{ m}
    Kipenyo D=25 cm=25100 m=0.25 mD = 25 \text{ cm} = \frac{25}{100} \text{ m} = 0.25 \text{ m}
    Kisha, kokotoa rediasi (rr):
    r=D2=0.25 m2=0.125 mr = \frac{D}{2} = \frac{0.25 \text{ m}}{2} = 0.125 \text{ m}

  2. Kokotoa Eneo la Jumla la Uso (Total Surface Area) la silinda.

    Fomula ya eneo la jumla la uso wa silinda imara ni A=2πrh+2πr2A = 2\pi r h + 2\pi r^2.
    A=2π(0.125 m)(2.5 m)+2π(0.125 m)2A = 2\pi (0.125 \text{ m})(2.5 \text{ m}) + 2\pi (0.125 \text{ m})^2
    A=2π(0.3125 m2)+2π(0.015625 m2)A = 2\pi (0.3125 \text{ m}^2) + 2\pi (0.015625 \text{ m}^2)
    A=0.625π m2+0.03125π m2A = 0.625\pi \text{ m}^2 + 0.03125\pi \text{ m}^2
    A=(0.625+0.03125)π m2A = (0.625 + 0.03125)\pi \text{ m}^2
    A=0.65625π m2A = 0.65625\pi \text{ m}^2
    Kutumia π≈3.14159\pi \approx 3.14159:
    A≈0.65625×3.14159 m2A \approx 0.65625 \times 3.14159 \text{ m}^2
    A≈2.0617 m2A \approx 2.0617 \text{ m}^2

    Eneo la Jumla la Uso ni: 2.0617 m2\boxed{\text{2.0617 m}^2}

  3. Kokotoa Kiasi (Volume) cha shaba kwenye bomba.

    Fomula ya kiasi cha silinda imara ni V=πr2hV = \pi r^2 h.
    V=π(0.125 m)2(2.5 m)V = \pi (0.125 \text{ m})^2 (2.5 \text{ m})
    V=π(0.015625 m2)(2.5 m)V = \pi (0.015625 \text{ m}^2) (2.5 \text{ m})
    V=0.0390625π m3V = 0.0390625\pi \text{ m}^3
    Kutumia π≈3.14159\pi \approx 3.14159:
    V≈0.0390625×3.14159 m3V \approx 0.0390625 \times 3.14159 \text{ m}^3
    V≈0.1227 m3V \approx 0.1227 \text{ m}^3

    Kiasi cha shaba kwenye bomba ni: 0.1227 m3\boxed{\text{0.1227 m}^3}

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