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
Here's the solution for Question 7: a) Step 1: Identify the given dimensions. Length (L) = 12 cm, Width (W) = 5 cm, Height (H) = 8 cm. Step 2: Substitute the dimensions into the Total Surface Area (TSA) formula. TSA = 2(LW + WH + LH) TSA = 2((12 cm × 5 cm) + (5 cm × 8 cm) + (12 cm × 8 cm)) Step 3: Calculate the products and sum them. TSA = 2(60 cm^2 + 40 cm^2 + 96 cm^2) TSA = 2(196 cm^2) Step 4: Calculate the total surface area. TSA = 392 cm^2 The Total Surface Area is 392 cm^2. b) Step 1: Identify the given dimensions. Length (L) = 12 cm, Width (W) = 5 cm, Height (H) = 8 cm. Step 2: Substitute the dimensions into the volume (V) formula. V = L × W × H V = 12 cm × 5 cm × 8 cm Step 3: Calculate the volume. V = 60 cm^2 × 8 cm V = 480 cm^3 The volume of the rectangular prism is 480 cm^3. c) Step 1: Determine the new dimensions by doubling the original dimensions. New Length (L') = 2 × 12 cm = 24 cm New Width (W') = 2 × 5 cm = 10 cm New Height (H') = 2 × 8 cm = 16 cm Step 2: Calculate the new volume (V') using the new dimensions. V' = L' × W' × H' V' = 24 cm × 10 cm × 16 cm V' = 240 cm^2 × 16 cm V' = 3840 cm^3 The new volume is 3840 cm^3. Step 3: Calculate the ratio of the new volume to the original volume. Ratio = New VolumeOriginal Volume Ratio = 3840 cm^3480 cm^3 Ratio = 8 The ratio of new volume to original volume is 8. 3 done, 2 left today. You're making progress.