Example Question - calculating surface area
Here are examples of questions we've helped users solve.
Calculating the Surface Area of a Liquid Reached by a Stone
<p>Функция высоты камня над поверхностью воды зависит от времени по следующей формуле:</p> <p>\( H(t) = 16 - 2t^2 \)</p> <p>Чтобы узнать, через сколько секунд камень достигнет поверхности воды, нам нужно определить время \( t \), когда \( H(t) = 0 \):</p> <p>\( 0 = 16 - 2t^2 \)</p> <p>\( 2t^2 = 16 \)</p> <p>\( t^2 = 8 \)</p> <p>\( t = \sqrt{8} \)</p> <p>\( t = 2\sqrt{2} \) секунды</p> <p>Ответ: камень достигнет поверхности воды через \( 2\sqrt{2} \) секунды.</p>
Calculating Surface Area of a Composite Figure
To calculate the surface area of this composite figure, we should break it down into its component rectangles and calculate the area of each, making sure not to count any hidden surfaces. First, let's consider the larger cuboid on the left: - It has two sides that are 16 in. by 8 in. - It has two sides that are 16 in. by 8 in. (top and bottom). - It has two sides that are 16 in. by 8 in. (front and back). Next, we consider the smaller cuboid on the right: - It has two sides that are 8 in. by 6 in. (left and right side, but the left side overlaps with the larger cuboid, so we only consider the right side). - It has a top side that is 8 in. by 6 in. - It has a front side that is 6 in. by 8 in. - It does not have a visible back side because it is covered by the larger cuboid. - It has a bottom side that is 8 in. by 6 in. Now, we will calculate the areas of all the visible sides and sum them up: Larger cuboid: - 2 sides (front and back): 2 * (16 in * 8 in) = 256 in² * 2 = 512 in² - 2 sides (left and right): 2 * (16 in * 8 in) = 256 in² * 2 = 512 in² - But we need to subtract the area where the smaller cuboid overlaps which is 6 in * 8 in = 48 in² Smaller cuboid: - 1 side (right side): 8 in * 6 in = 48 in² - 1 top side: 8 in * 6 in = 48 in² - 1 front side: 8 in * 6 in = 48 in² - Bottom side (but it is fully overlapping with the larger cuboid, so it's not added to the surface area) Adding all the calculated areas: Total surface area = (512 in² + 512 in² - 48 in²) + (48 in² + 48 in² + 48 in²) Total surface area = 1024 in² - 48 in² + 144 in² Total surface area = 1120 in² So, the surface area of the figure is 1120 square inches.
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