Question

A tea infuser in the shape of a right triangular pyramid is 8 cm tall and has a base area of 12 cm².

What is the volume of the tea infuser in cubic centimeters?
Responses
A 96 cm³96 cm³
B 192 cm³192 cm³
C 32 cm³32 cm³
D 48 cm³

Answer 1

[AI-generated answer — Bot GPT 3.5]

The formula for the volume of a right triangular pyramid is V = (1/3) * base area * height.

Plugging in the values given:
V = (1/3) * 12 cm² * 8 cm
V = (1/3) * 96 cm³
V = 32 cm³

Therefore, the correct answer is C) 32 cm³.

Answer 2

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Question
A swimming pool is shaped like a right rectangular prism with length 20 feet, height 8 feet, and width 15 feet. If the pool's water line is one foot below the top of the pool, find the volume of water in the pool.
Responses
A 2,000 cubic feet2,000 cubic feet
B 2,100 cubic feet2,100 cubic feet
C 2,250 cubic feet2,250 cubic feet
D 2,400 cubic feet

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the volume of the water in the pool, we need to first find the volume of the entire pool and then subtract the volume of the portion above the water line.

The volume of a right rectangular prism is calculated as V = length * width * height.

Given:
Length = 20 feet
Height = 8 feet
Width = 15 feet

Volume of the entire pool:
V = 20 ft * 15 ft * 8 ft
V = 2400 cubic feet

The volume of the portion of the pool above the water line is:
Volume above water line = 20 ft * 15 ft * 1 ft (height above water line)
Volume above water line = 300 cubic feet

Therefore, the volume of water in the pool is:
Volume of water = Total volume - Volume above water line
Volume of water = 2400 cubic feet - 300 cubic feet
Volume of water = 2100 cubic feet

Therefore, the correct answer is B) 2,100 cubic feet.