#1 What is the volume of a pyramid with base area B = 6 ft2 and height h = 13 ft? A. 26 ft3 B. 39 ft3 C. 52 ft3 D. 78 ft3 #2 The base of a square pyramid has a side length of 6 inches. The height of the pyramid is 12 inches. What is the volume of the pyramid? A. 144 in3 B. 36 in3 C. 72 in3 D. 108 in3

#1 is A #2 is also A #3 is D #4 is C #5 is also C

Answered by kittysoftpaws | 2024-06-10

1). Option A is correct.
2). option A is correct.
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Answered by aquialaska | 2024-06-12

The volume of the first pyramid is 26 ft³, corresponding to option A. The volume of the second pyramid is 144 in³, also corresponding to option A.
; 1).
Given: Area of Base (B) = 6 ft² and height (h) = 13 ft.
The volume of a pyramid can be calculated using the formula:
V o l u m e = 3 1 ​ × B a se A re a × h e i g h t
Substituting the values, we get:
V o l u m e = 3 1 ​ × 6 × 13
Calculating this:
V o l u m e = 3 1 ​ × 78 = 26 f t 3
Therefore, the answer for the first question is Option A: 26 ft³.
2).
The base of the square pyramid has a side length of 6 inches. The height (h) of the pyramid is 12 inches.
First, we need to calculate the area of the base:
B a se A re a = s i d e × s i d e = 6 × 6 = 36 in c h e s 2
Now, we can calculate the volume using the same formula:
V o l u m e = 3 1 ​ × B a se A re a × h e i g h t
Substituting the values, we get:
V o l u m e = 3 1 ​ × 36 × 12
Calculating this:
V o l u m e = 3 1 ​ × 432 = 144 i n 3
Therefore, the answer for the second question is Option A: 144 in³.
[section_start id=examples_and_evidence]
For example, if you have a pyramid with a base area of 12 ft² and a height of 9 ft, you would calculate the volume as (1/3) * 12 * 9 = 36 ft³.
The formula for the volume of a pyramid is derived from geometric principles and is consistent across various mathematical texts.

Answered by aquialaska | 2025-04-09