Carla is baking brownies for the school bake sale. The batter fills a pan that is 20 cm long by 16 cm wide by 4.4 cm deep.Then,
she changes pans so that the new one is 20 by 20 by 5 cm deep. How far is the batter now from the top? Round to the nearest tenth. Also, pleaseshow work. That way I can look at how the problem is solved. Thank you!
The volume of the first pan is (length x width x depth) =
(20cm x 16cm x 4.4cm) = 1408 cm³ .
The batter fills it, so we know there is 1408 cm³ of batter.
Somehow, Carla manages to transfer every drop and smidgen of batter to the new pan, leaving not a single drip of it in the first pan. So we know that there is 1408 cm³ of batter in the new pan. It will spread out to fill the whole length and width of the new pan, and we're to calculate how deep it will be.
(length x width x depth) = 1408 cm³
(20cm x 20cm) x (depth) = 1408 cm³
(400 cm²) x (depth) = 1408 cm³
Divide each side by 400cm² : depth = 1408 cm³ / 400cm²
= 3.52 cm
Since the new pan is 5 cm deep, this works. The batter doesn't overfill it and glurb out over the top and all over the counter.
The question asked how far the batter is <em>from the top of the pan</em>.
The pan is 5 cm deep. The batter is 3.52cm deep.
The batter comes up to (5 - 3.52) = 1.48 cm from the top of the pan.
Rounded to the nearest tenth of a cm, that's <em>1.5 cm </em>from the top.
Dilations which reduce or enlarge an object. Translations which move the object from one part on the graph to another. I have also learned about how to construct a perpendicular bisector.
