As runners in a marathon go by, volunteers hand them small cone shaped cups of water. The cups have the dimensions shown. Abigail sloshes \dfrac23 3
2
start fraction, 2, divided by, 3, end fraction of the water out of her cup before she gets a chance to drink any.
What is the volume of water remaining in Abigail's cup?
Answers
Consider the attached figure required to solve this problem.
Given:
As runners in a marathon go by, volunteers hand them small cone-shaped cups of water having the dimensions of height 8 cm and radius 3 cm.
Abigail sloshes 2/3 fraction of the water out of her cup before she gets a chance to drink any.
To find:
What is the volume of water remaining in Abigail's cup?
Solution:
First, we need to find the volume of cone-shaped cup.
The volume of cone = πr²h/3
where r = radius of the cone
h = height of the cone.
From given, we have,
r = radius of the cone = 3 cm
h = height of the cone = 8 cm
The volume of cone = The initial volume of water in that cone cup.
Therefore, the volume of water remaining in Abigail's cup after she sloshes 2/3 fraction of the water out of her cup is given by,
Volume (remaining) = Volume (total) - Volume (2/3 rd)
= πr²h/3 - 2/3 × πr²h/3
= πr²h/3 (1 - 2/3)
= πr²h/3 (1/3)
= (π × r² × h) / (3 × 3)
= (22/7 × 3² × 8) / (3²)
= 22/7 × 8
= 25.14 cm³
Therefore, 25.14 cm³ is the volume of water remaining in Abigail's cup.
Answer:
8π
Step-by-step explanation: