Archeologists discover four outer walls of an ancient building, as shown.
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Question:
The volume of a right circular cone with both diameter and height equal to h is 250/7 cm³.
What is the value of h?
Answer:
A. 5
Step-by-step explanation:
Given
Solid Shape: Cone
Volume = 250/7
Diameter = Height
Required
Find the height of the cone
Provided that the diameter (D) and the height (h) are equal; This implies that
D = h ------ (1)
Also, Diameter (D) = 2 * Radius (r)
D = 2r
Substitute 2r for D in (1)
2r = h
Multiply both sides by ½
½ * 2r = ½ * h
r = ½h
Volume of a cone is calculated by;
Volume = ⅓πr²h
⅓πr²h = 250/7
Substitute ½h for r
Take π as 22/7, the expression becomes
Open the bracket
Multiply both sides by 7
Multiply both sides by 3
Multiply both sides by 4
Divide both sides by 22
Take cube root of both sides
(Approximated)