Surface area of a box without a top năm 2024
We explain how to find the surface area of a cuboid, or box, and provide a quick calculator to work it out for you, step-by-step. Show
Our calculator will find the surface area of both closed and open boxes. There are also lots of worked examples and some worksheets for you to practice this skill. Quicklinks to ... Surface Area of a Box CalculatorThis calculator finds the surface area of a cuboid (or box) when the side lengths are known. How the Calculator Works
Surface Area of a Box (or Cuboid) FormulaBelow are the formulas for the surface area of both a closed box and an open box. An open box is basically a normal box which does not have a lid so it is open at the top. The formula for the surface area of a closed box (or cuboid) is: \[ A = 2lw + 2lh + 2wh \; \] where l is the length, w is the width, and h is the height of the cuboid The formula for the surface area of an open box (with no lid) is: \[ A = lw + 2lh + 2wh \; \] Surface Area of a Box ExplainedA box, or cuboid, is a 3-dimensional shape made up of 6 faces, all of which are rectangles. Each face of the box has an opposite identical face which we can see clearly if we look at the net. So a box has 3 separate pairs of identical faces. The surface area of the box is equal to the total of all the areas of the rectangular faces. So the total surface area of the box is: \[ A = lw + lw + lh + lh + wh + wh = 2lw + 2lh + 2wh. \] Surface Area of a Box ExamplesSurface Area of a Box Example 1Find the surface area of the box below. The box has the following dimensions:
The surface area of the box is: \[ A = 2lw + 2lh + 2wh \; \] where l is the length, w is the width, and h is the height of the box So if we substitute the values of the length and width into this equation, we get: \[ A = 2 \cdot 7 \cdot 3 + 2 \cdot 7 \cdot 5 + 2 \cdot 3 \cdot 5 = 42 + 70 + 30 = 142 \] The surface area of the box is 142 cm2. Surface Area of a Box Example 2Find the surface area of the box below. The box has the following dimensions:
The surface area of the box is: \[ A = 2lw + 2lh + 2wh \; \] So if we substitute the values of the length and width into this equation, we get: \[ A = 2 \cdot 12 \cdot 5 + 2 \cdot 12 \cdot 3 + 2 \cdot 5 \cdot 3 = 120 + 72 + 30 = 222 \] The surface area of the box is 222 in2. Surface Area of a Box Example 3Find the surface area of the box below, giving your answer to 1 decimal place. The box has the following dimensions:
The surface area of the box is: \[ A = 2lw + 2lh + 2wh \; \] So if we substitute the values of the length and width into this equation, we get: \[ A = 2 \cdot 5.6 \cdot 4.3 + 2 \cdot 5.6 \cdot 2.5 + 2 \cdot 4.3 \cdot 2.5 = 48.16 + 28 + 21.5 = 97.66 \] The surface area of the box is 97.7 cm2 to 1 decimal place. Surface Area of a Box Example 4Find the surface area of the open box below. The box has the following dimensions:
The formula for the surface area of an open box is: \[ A = lw + 2lh + 2wh \; \] So if we substitute the values of the length and width into this equation, we get: \[ A = 6 \cdot 3 {1 \over 2} + 2 \cdot 6 \cdot 2 {1 \over 2} + 2 \cdot 3 {1 \over 2} \cdot 2 {1 \over 2} = 21 + 30 + 17 {1 \over 2} = 68 {1 \over 2} \] The surface area of the box is 68 ½ in2. Surface Area of a Cuboid WorksheetsWe have created two worksheets for you to practice this skill. The first sheet involves finding the surface area of different cuboids with simple numerical values for the side measurements. The second sheet is the same as the first but has decimal and fractional values for the side measurements.
More Recommended Math ResourcesTake a look at some more of our worksheets similar to these. More Surface Area Worksheets and Support Pages
More Area Support and ResourcesWe have a range of other area worksheets and support pages for a range of different 2d shapes.
More Area & Volume CalculatorsWe have a range of area and volume calculators to help you find the area and volumes of a range of different 2d and 3d shapes. Each calculator page comes with worked examples, formulas and practice worksheets.
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How to Print or Save these sheets 🖶 Need help with printing or saving? Follow these 3 steps to get your worksheets printed perfectly!
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Math-Salamanders.comThe Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources. We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page. What is the surface area of a closed box?Surface area is total area on the surface of a three-dimensional shape. To find the surface area of a cuboid which has 6 rectangular faces, add the areas of all 6 faces. Or, you can label the length (l), width (w), and height (h) of the cuboid and use the formula: surface area (SA)=2lw+2lh+2hw. |