This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Haya Dennis, twende kazi! 13. a) A cone has a radius of 3m and a height of 4m. Calculate its surface area and volume. Step 1: Kokotoa urefu wa slant (l) kwa kutumia Theorem ya Pythagoras. l = sqrt(r^2 + h^2) l = sqrt((3 m))^2 + (4 m)^2 l = sqrt(9 m)^2 + 16 m^2 l = sqrt(25 m)^2 l = 5 m Step 2: Kokotoa eneo la uso (A) la koni. Fomula ni jumla ya eneo la duara la chini na eneo la uso wa kando. A = r^2 + r l A = (3 m)^2 + (3 m)(5 m) A = 9 m^2 + 15 m^2 A = 24 m^2 Step 3: Kokotoa ujazo (V) wa koni. V = (1)/(3) r^2 h V = (1)/(3) (3 m)^2 (4 m) V = (1)/(3) (9 m^2) (4 m) V = 12 m^3 Jibu la Mwisho: Eneo la uso = 24 m^2, Ujazo = 12 m^3 b) A sphere has a radius of 3m. Finds its Surface area and volume. Step 1: Kokotoa eneo la uso (A) la tufe. A = 4 r^2 A = 4 (3 m)^2 A = 4 (9 m^2) A = 36 m^2 Step 2: Kokotoa ujazo (V) wa tufe. V = (4)/(3) r^3 V = (4)/(3) (3 m)^3 V = (4)/(3) (27 m^3) V = 4 (9 m^3) V = 36 m^3 Jibu la Mwisho: Eneo la uso = 36 m^2, Ujazo = 36 m^3 3 done, 2 left today. You're making progress.