Answer:
Step-by-step explanation:
Given
Midpoint, T
Required
Determine PT
First, the value of x has to be calculated;
Since T is the midpoint, then:
This implies
Solve for x
Length PQ can then be calculated using:
Collect Like Terms
Substitute 6 for x
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)