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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Step 1: Round 179.35 to one significant figure. The first significant digit is 1. The next digit is 7, which is 5 or greater, so we round up the first significant digit. 179.35 ≈ 200 Step 2: Round 0.0496 to one significant figure. The first non-zero digit is 4. The next digit is 9, which is 5 or greater, so we round up the first significant digit. 0.0496 ≈ 0.05 Step 3: Multiply the rounded values to estimate the product. 200 × 0.05 = 10 The estimated value is 10. --- a) A solid cuboid measures 5 cm by 2 cm by x cm. Form an expression, in terms of x, for the total surface area of the cuboid. Step 1: Identify the dimensions of the cuboid. Length (l) = 5 cm Width (w) = 2 cm Height (h) = x cm Step 2: Write the formula for the total surface area of a cuboid. The total surface area (SA) of a cuboid is given by: SA = 2(lw + lh + wh) Step 3: Substitute the given dimensions into the formula. SA = 2((5)(2) + (5)(x) + (2)(x)) SA = 2(10 + 5x + 2x) SA = 2(10 + 7x) SA = 20 + 14x The expression for the total surface area is 20 + 14x cm^2. --- b) (i) The total surface area of the cuboid is 62 cm^2. Form an equation in x. Step 1: Use the expression for the total surface area from part (a). The expression for the total surface area is 20 + 14x. Step 2: Set the expression equal to the given total surface area. 20 + 14x = 62 The equation in x is 20 + 14x = 62. --- b) (ii) Solve the equation in (b)(i) to find the value of x. Step 1: Write the equation from part (b)(i). 20 + 14x = 62 Step 2: Subtract 20 from both sides of the equation. 14x = 62 - 20 14x = 42 Step 3: Divide both sides by 14 to solve for x. x = (42)/(14) x = 3 The value of x is 3. --- 9 (a) A solid object has a mass of 300 kg and a volume of 2 m^3. Calculate the density of the object. Step 1: Write the formula for density. Density () is calculated as mass (m) divided by volume (V): = (m)/(V) Step 2: Substitute the given values for mass and volume. Mass (m) = 300 kg Volume (V) = 2 m^3 = 300 kg2 m^3 Step 3: Calculate the density. = 150 kg/m^3 The density of the object is 150 kg/m^3. 3 done, 2 left today. You're making progress.