A metal sphere of diameter 15 cm is melted down and recast into hollow cylindrical pipe of external radius 7.5 cm and internal radius 3 cm. In the process 12% of the metal is lost. Calculate the volume of metal used to make the pipe.

Haya, hebu tutatue swali hili hatua kwa hatua. a) Kokotoa ujazo wa chuma kilichotumika kutengeneza bomba. Step 1: Kokotoa rediasi ya tufe. Rediasi ya tufe R_tufe ni nusu ya kipenyo. R_tufe = 15 cm2 = 7.5 cm Step 2: Kokotoa ujazo wa tufe la awali. Fomula ya ujazo wa tufe ni V = (4)/(3) R^3. V_tufe = (4)/(3) (7.5 cm)^3 V_tufe = (4)/(3) (421.875 cm^3) V_tufe = 562.5 cm^3 Step 3: Kokotoa ujazo wa chuma kilichotumika baada ya kupoteza 12%. Asilimia ya chuma iliyotumika ni 100\% - 12\% = 88\%. V_iliyotumika = 0.88 × V_tufe V_iliyotumika = 0.88 × 562.5 cm^3 V_iliyotumika = 495 cm^3 Ujazo wa chuma kilichotumika kutengeneza bomba ni 495 cm^3. b) Kokotoa eneo la msalaba la chuma kwenye bomba. Step 1: Tambua rediasi ya ndani na ya nje ya bomba. Rediasi ya nje R = 3 cm. Rediasi ya ndani r = 2.3 cm. Step 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. A_msalaba = R^2 - r^2 A_msalaba = (R^2 - r^2) A_msalaba = ((3 cm)^2 - (2.3 cm)^2) A_msalaba = (9 cm^2 - 5.29 cm^2) A_msalaba = (3.71 cm^2) Eneo la msalaba la chuma kwenye bomba ni 3.71 cm^2. c) Kokotoa urefu wa bomba kwa mita, kwa sehemu mbili za desimali. Step 1: Tumia ujazo wa chuma kilichotumika na eneo la msalaba kukokotoa urefu wa bomba. Ujazo wa bomba ni sawa na ujazo wa chuma kilichotumika. V_bomba = A_msalaba × h Ambapo h ni urefu wa bomba. 495 cm^3 = 3.71 cm^2 × h Step 2: Tafuta h. Gawanya pande zote mbili kwa 3.71 cm^2: h = 495 cm^33.71 cm^2 h = (495)/(3.71) cm h ≈ 133.42318 cm Step 3: Badilisha urefu kutoka sentimita kwenda mita na uzungushe kwa sehemu mbili za desimali. Kumbuka kuwa 1 m = 100 cm. h_mita = 133.42318 cm100 cm/m h_mita ≈ 1.3342318 m Kuzungusha kwa sehemu mbili za desimali: h_mita ≈ 1.33 m Urefu wa bomba ni 1.33 m. Tuma swali linalofuata 📸