Stephanie is going to form a clay model of the moon. The model will have a diameter of 2 feet, and the clay she will use comes in containers as described below. What is the least number of containers Stephanie will need in order to complete the model?
a.3
b.11
c.16
d.22
Please help i think its a but im not sure.
What shape are the containers?
Where is their description?
Are their dimensions in inches or centimeters or miles or what?
the containers are cylinder shaped, 1/2 ft tall, and 1 ft diameter.
To determine the least number of containers Stephanie will need, we need to calculate the volume of the clay required and compare it to the volume of each container.
1. Start by calculating the volume of the moon model using the formula for the volume of a sphere:
V = (4/3)πr³
Given that the diameter is 2 feet, we can calculate the radius (r) by dividing the diameter by 2:
r = 2 feet ÷ 2 = 1 foot
Now, we can calculate the volume (V) of the moon model:
V = (4/3)π(1 foot)³ = (4/3)π(1 foot)³ ≈ 4.18879 cubic feet
2. Next, compare the volume of the moon model (4.18879 cubic feet) to the volume of each container.
a. If each container can hold less than 4.18879 cubic feet, it will be insufficient, and Stephanie will need more than 1 container.
b. If each container can hold precisely 4.18879 cubic feet, she will need 1 container.
c. If each container can hold more than 4.18879 cubic feet, she will only need 1 container.
Looking at the options given:
a. 3 containers: Stephanie would need at least 3 containers if each container can hold less than 4.18879 cubic feet. Therefore, option a is a possibility.
b. 11 containers: Stephanie would require 11 containers if each container can hold exactly 4.18879 cubic feet. Therefore, option b is a possibility.
c. 16 containers: Stephanie would need at least 16 containers if each container can hold less than 4.18879 cubic feet. Therefore, option c is a possibility.
d. 22 containers: Stephanie would need at least 22 containers if each container can hold less than 4.18879 cubic feet. Therefore, option d is a possibility.
We cannot determine the correct answer without additional information about the volume each container can hold.
To determine the least number of containers Stephanie will need to complete the clay model of the moon, we need to calculate the volume of the model and divide it by the volume of each container.
The volume of a sphere (like the clay model) is given by the formula: V = (4/3)πr³, where V is the volume and r is the radius.
Given that the diameter of the model is 2 feet, the radius can be calculated as half of the diameter, or 1 foot.
Plugging the radius value into the volume formula, we get:
V = (4/3)π(1)³
V = (4/3)π(1)
V = (4/3)π
Now, let's consider the volumes of the containers. Since the information about the container volumes is not provided, we cannot determine which option is correct. Can you provide the container volumes for each option?