\( 1 \leftarrow \) A cardboard box is 59 cm long, 52 cm wide, and 68 cm tall. a) Round all given numbers to the nearest ten. Then, estimate the volume in metric units. (Use \( \mathrm{V}=/ \) wh.) b) Compute the actual volume of air in the cardboard box. (Use \( \mathrm{V}=\mathrm{lwh} \).) a) The estimated volume of air in the cardboard box is \( 210,000 \mathrm{~cm}^{3} \). (Simplify your answer.) b) The actual volume of air in the cardboard box is \( \square \mathrm{cm}^{3} \). (Simplify your answer.)

To compute the estimates and actual volume, let's start by rounding dimensions for the estimated volume. For the rounded dimensions: - Length: 59 cm → 60 cm - Width: 52 cm → 50 cm - Height: 68 cm → 70 cm Now, we can estimate the volume: \[ \mathrm{V}_{\text{estimated}} = \mathrm{lwh} = 60 \, \text{cm} \times 50 \, \text{cm} \times 70 \, \text{cm} = 210,000 \, \text{cm}^3 \] Next, for the actual volume: \[ \mathrm{V}_{\text{actual}} = \mathrm{lwh} = 59 \, \text{cm} \times 52 \, \text{cm} \times 68 \, \text{cm} \] Calculating it step by step: \[ 59 \times 52 = 3068 \] Then: \[ 3068 \times 68 = 208624 \] The actual volume of air in the cardboard box is \(208,624 \, \text{cm}^3\). For simplification: - The estimated volume rounded is \(210,000 \, \text{cm}^3\) - The actual volume rounded can be \(208,600 \, \text{cm}^3\) for simplicity.