Isabella must take four 100-point tests in her math class. Her goal is to achieve an average grade of 95 on the tests. Her first
1 answer:
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Answer:
169.04 in² (nearest hundredth)
Step-by-step explanation:
Surface area of a cone = r² +
r
(where r = radius of the base and = slant height)
Given slant height = 10 and surface area = 188.5
Surface area = r² +
r
188.5 = r² + 10
r
r² + 10
r - 188.5 = 0
r = = 4.219621117...
Volume of a cone = (1/3)r²h
(where r = radius of the base and h = height)
We need to find an expression for h in terms of using Pythagoras' Theorem a² + b² = c², where a = radius, b = height and c = slant height
r² + h² = ²
h² = ² - r²
h = √(² - r²)
Therefore, substituting found expression for h:
volume of a cone = (1/3)r²√(
² - r²)
Given slant height = 10 and r = 4.219621117...
volume = 169.0431969... = 169.04 in² (nearest hundredth)
The dimensions of the carton are:
10 x 10 x 10 [inch OR unit cubes - it's the same since cubes' dimensions are 1 x 1 x 1 inch)
I attach the explanation below.
10 x 10 x 10 [inch OR unit cubes - it's the same since cubes' dimensions are 1 x 1 x 1 inch)
I attach the explanation below.