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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Hey LUCKY, good to see you again. a) To determine how much money Okello earned, we first calculate the volume of the ice cream bucket, then the volume of one small tin, find out how many tins can be filled, and finally calculate the total earnings. Step 1: Calculate the volume of the frustum (ice cream bucket). The bucket is a frustum with top diameter 48 cm (radius R = 24 cm), bottom diameter 14 cm (radius r = 7 cm), and height H = 20 cm. The volume of a frustum is given by V = (1)/(3) H (R^2 + Rr + r^2). V_bucket = (1)/(3) (20 cm) ((24 cm)^2 + (24 cm)(7 cm) + (7 cm)^2) V_bucket = (20)/(3) (576 + 168 + 49) cm^3 V_bucket = (20)/(3) (793) cm^3 = (15860)/(3) cm^3 Step 2: Calculate the volume of one cylindrical tin. Each tin is a cylinder with diameter 7 cm (radius r_tin = 3.5 cm) and height h_tin = 5 cm. The volume of a cylinder is given by V = r^2 h. V_tin = (3.5 cm)^2 (5 cm) V_tin = (12.25) (5) cm^3 = 61.25 cm^3 Step 3: Determine the number of small tins that can be filled. The number of tins is the total volume of ice cream divided by the volume of one tin. We take the floor since only full tins are sold. N = V_bucketV_tin = (15860)/(3) cm^361.25 cm^3 N = (15860)/(3 × 61.25) = (15860)/(183.75) ≈ 86.31 So, 86 full tins can be filled. Step 4: Calculate the total money earned. Each tin is sold for UGX 2,000. Total money = 86 × UGX 2,000 = UGX 172,000 Okello earned UGX 172,000. b) To determine how close Okello moved towards the tree, we use trigonometry to find his initial and final distances from the tree. Step 1: Determine the effective height of the mango tree. The height of the tree is 25 m, and Okello's height is 1.5 m. The effective height for the angle of elevation is the height of the mango above Okello's eye level. H_eff = 25 m - 1.5 m = 23.5 m Step 2: Calculate Okello's initial horizontal distance from the tree. The initial angle of elevation is 32^. Let D_1 be the initial horizontal distance. () = oppositeadjacent (32^) = 23.5 mD_1 D_1 = 23.5 m(32^) ≈ 23.5 m0.62487 ≈ 37.607 m Step 3: Calculate Okello's final horizontal distance from the tree. The angle of elevation increased by 18^, so the final angle _2 = 32^ + 18^ = 50^. Let D_2 be the final horizontal distance. (50^) = 23.5 mD_2 D_2 = 23.5 m(50^) ≈ 23.5 m1.19175 ≈ 19.719 m Step 4: Calculate how close Okello moved towards the tree. The distance Okello moved is the difference between the initial and final distances. Distance moved = D_1 - D_2 ≈ 37.607 m - 19.719 m ≈ 17.888 m Okello moved approximately 17.89 m closer to the tree. Send me the next one 📸