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Scientists create a futuristic soap bubble in the shape of a box with a square base that contains a fixed volume of air. Specifically, the soap bubble contains 3 cm³ of air. (a) Draw a picture. (b) If the base of the soap bubble box has a side length of 2 cm, what is the surface area of the soap bubble? (c) If the base of the soap bubble box has a side length of x cm, what is the surface area of the soap bubble? (d) Use differentials to approximate the change in surface area if the side length of the base is shrunk from 2 cm to 1.99 cm.

Scientists create a futuristic soap bubble in the shape of a box with a square base that contains a fixed volume of air. Specifically, the soap bubble contains 3 cm³ of air. (a) Draw a picture. (b) If the base of the soap bubble box has a side length of 2 cm, what is the surface area of the soap bubble? (c) If the base of the soap bubble box has a side length of x cm, what is the surface area of the soap bubble? (d) Use differentials to approximate the change in surface area if the side length of the base is shrunk from 2 cm to 1.99 cm.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.1: Prisms, Area And Volume
Problem 37E: Zaidah plans a raised flower bed 2 ft high by 12 ft wide by 15 ft long. The mulch, soil, and peat...
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Scientists create a futuristic soap bubble in the shape of a box with a square base that contains a fixed volume of air. Specifically, the soap bubble contains 3 cm of air. (a) Draw a picture. (b) If the base of the soap bubble box has a side length of 2 cm, what is the surface area of the soap bubble? (c) If the base of the soap bubble box has a side length of x cm, what is the surface area of the soap bubble? (d) Use differentials to approximate the change in surface area if the side length of the base is shrunk from 2 cm to 1.99 cm.
Transcribed Image Text:Scientists create a futuristic soap bubble in the shape of a box with a square base that contains a fixed volume of air. Specifically, the soap bubble contains 3 cm of air. (a) Draw a picture. (b) If the base of the soap bubble box has a side length of 2 cm, what is the surface area of the soap bubble? (c) If the base of the soap bubble box has a side length of x cm, what is the surface area of the soap bubble? (d) Use differentials to approximate the change in surface area if the side length of the base is shrunk from 2 cm to 1.99 cm.
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