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.
ScanSolve AI Answer
Step 1: Calculate the volume of the external hemisphere. The formula for the volume of a hemisphere is V = (2)/(3) r^3. Given external radius R = 21 cm. V_ext = (2)/(3) (21 cm)^3 V_ext = (2)/(3) (9261 cm^3) V_ext = 6174 cm^3 Step 2: Calculate the volume of the internal hemisphere. Given internal radius r = 17.5 cm. V_int = (2)/(3) (17.5 cm)^3 V_int = (2)/(3) (5359.375 cm^3) V_int = (10718.75)/(3) cm^3 Step 3: Calculate the volume of the material. The volume of the material is the difference between the external and internal volumes. V_material = V_ext - V_int V_material = 6174 cm^3 - (10718.75)/(3) cm^3 V_material = ( (18522 - 10718.75)/(3) ) cm^3 V_material = (7803.25)/(3) cm^3 V_material ≈ 2601.0833 cm^3 V_material ≈ 8171.09 cm^3 Step 4: Calculate the mass of the bowl in grams. The formula for mass is M = × V. Given density = 9.3 g/cm^3. M = 9.3 g/cm^3 × (7803.25)/(3) cm^3 M = 3.1 × 7803.25 g M = 24189.975 g M ≈ 75997.14 g Step 5: Convert the mass to kilograms. There are 1000 grams in 1 kilogram. M_kg = 75997.14 g1000 M_kg ≈ 75.997 kg Rounding to one decimal place: M_kg ≈ 76.0 kg The mass of the bowl is 76.0 kg. Step 1: Convert the movie duration from decimal hours to hours and minutes. The movie lasted 2.3 hours. This is 2 full hours and 0.3 of an hour. To convert 0.3 hours to minutes: 0.3 hours × 60 minutes/hour = 18 minutes So, the movie duration is 2 hours and 18 minutes. Step 2: Subtract the duration from the end time to find the start time. The movie ended at 0110h (1:10 AM). We need to subtract 2 hours and 18 minutes from 0110h. First, subtract 2 hours: 0110h - 2 hours = 2310h (on the previous day) Now, subtract 18 minutes from 2310h: We have 10 minutes, so we need to borrow 1 hour (60 minutes) from the hours. 23h 10min → 22h (60+10)min = 22h 70min 22h 70min - 18min = 22h 52min So, the start time is 2252h. The time on Ali's watch when the movie started was 2252h. 3 done, 2 left today. You're making progress.