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Calculate to 2 decimal places the length of the pipe in metres.

Mathematics

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2 parts
a

3.71π cm23.71 \pi \text{ cm}^2

b

1.33 m1.33 \text{ m}

Step-by-step solution

5 steps

Haya, hebu tuangalie kazi yako na tutatue maswali yaliyobaki.

Kutoka kwenye mahesabu yako ya awali, ujazo wa chuma kilichotumika kutengeneza bomba ni sahihi:

Viliyotumika=495π cm3V_{iliyotumika} = 495 \pi \text{ cm}^3

Part a· 2 steps

Kokotoa eneo la msalaba la chuma kwenye bomba.

  1. Tambua rediasi ya nje na ya ndani ya bomba.

    Rediasi ya nje R=3 cmR = 3 \text{ cm}.
    Rediasi ya ndani r=2.3 cmr = 2.3 \text{ cm}.

  2. Kokotoa eneo la msalaba la chuma.

    Eneo la msalaba la chuma ni tofauti kati ya eneo la duara la nje na eneo la duara la ndani.

    Amsalaba=πR2−πr2A_{msalaba} = \pi R^2 - \pi r^2 Amsalaba=π(R2−r2)A_{msalaba} = \pi (R^2 - r^2) Amsalaba=π((3 cm)2−(2.3 cm)2)A_{msalaba} = \pi ((3 \text{ cm})^2 - (2.3 \text{ cm})^2) Amsalaba=π(9 cm2−5.29 cm2)A_{msalaba} = \pi (9 \text{ cm}^2 - 5.29 \text{ cm}^2) Amsalaba=π(3.71 cm2)A_{msalaba} = \pi (3.71 \text{ cm}^2)

    Eneo la msalaba la chuma kwenye bomba ni 3.71π cm2\boxed{3.71 \pi \text{ cm}^2}.
    Jibu lako la 1.16π cm21.16 \pi \text{ cm}^2 lilikuwa si sahihi.

Part b

1.33 m1.33 \text{ m}

Kokotoa urefu wa bomba kwa mita, kwa sehemu mbili za desimali.

  1. Tumia ujazo wa chuma kilichotumika na eneo la msalaba kukokotoa urefu wa bomba.

    Ujazo wa bomba ni sawa na ujazo wa chuma kilichotumika.

    Vbomba=Amsalaba×hV_{bomba} = A_{msalaba} \times h

    Ambapo hh ni urefu wa bomba.

    495π cm3=3.71π cm2×h495 \pi \text{ cm}^3 = 3.71 \pi \text{ cm}^2 \times h

  2. Tafuta hh.

    Gawanya pande zote mbili kwa 3.71π cm23.71 \pi \text{ cm}^2:

    h=495π cm33.71π cm2h = \frac{495 \pi \text{ cm}^3}{3.71 \pi \text{ cm}^2} h=4953.71 cmh = \frac{495}{3.71} \text{ cm} h≈133.42318 cmh \approx 133.42318 \text{ cm}

  3. Badilisha urefu kutoka sentimita kwenda mita na uzungushe kwa sehemu mbili za desimali.

    Kumbuka kuwa 1 m=100 cm1 \text{ m} = 100 \text{ cm}.

    hmita=133.42318 cm100 cm/mh_{mita} = \frac{133.42318 \text{ cm}}{100 \text{ cm/m}} hmita≈1.3342318 mh_{mita} \approx 1.3342318 \text{ m}

    Kuzungusha kwa sehemu mbili za desimali:

    hmita≈1.33 mh_{mita} \approx 1.33 \text{ m}

    Urefu wa bomba ni 1.33 m\boxed{1.33 \text{ m}}.
    Jibu lako la 4.27 m4.27 \text{ m} lilikuwa si sahihi kwa sababu lilitokana na eneo la msalaba lisilo sahihi.

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