Question
The figure is made up of a cylinder and a cone.
What is the exact volume of the figure?
Enter your answer in the box.
ft3
There is a line in the middle the number is 5ft and then at the end of the line connects to other line going to the right and the number is 3ft. There is a 4 ft on the outside of the shape of the circle
What is the exact volume of the figure?
Enter your answer in the box.
ft3
There is a line in the middle the number is 5ft and then at the end of the line connects to other line going to the right and the number is 3ft. There is a 4 ft on the outside of the shape of the circle
Answers
GPT-4o mini
To calculate the exact volume of the figure made up of a cylinder and a cone, we need to gather the dimensions provided from your description:
1. The height of the cylinder (h_cyl) is given as 5 ft.
2. The radius of the circular base of both the cylinder and the cone (r) is given as half of the diameter. Since you stated there is a measurement of 3 ft at the end of a line going to the right, I'll assume this is the diameter of the circular base, so the radius \( r = \frac{3 \text{ ft}}{2} = 1.5 \text{ ft} \).
3. The height of the cone (h_cone) is not explicitly given, but letβs assume it to be the same as the height of the cylinder, which is 5 ft for this calculation.
### Volume of the Cylinder
The volume \( V_{cyl} \) of a cylinder is given by the formula:
\[
V_{cyl} = \pi r^2 h_{cyl}
\]
Substituting the values:
\[
V_{cyl} = \pi (1.5 \text{ ft})^2 (5 \text{ ft}) = \pi (2.25 \text{ ft}^2)(5 \text{ ft}) = 11.25\pi \text{ ft}^3
\]
### Volume of the Cone
The volume \( V_{cone} \) of a cone is given by the formula:
\[
V_{cone} = \frac{1}{3} \pi r^2 h_{cone}
\]
Substituting the values:
\[
V_{cone} = \frac{1}{3} \pi (1.5 \text{ ft})^2 (5 \text{ ft}) = \frac{1}{3}\pi (2.25 \text{ ft}^2)(5 \text{ ft}) = \frac{11.25\pi}{3} \text{ ft}^3 = 3.75\pi \text{ ft}^3
\]
### Total Volume of the Figure
To find the total volume \( V_{total} \) of the figure, we add the volumes of the cylinder and the cone:
\[
V_{total} = V_{cyl} + V_{cone} = 11.25\pi \text{ ft}^3 + 3.75\pi \text{ ft}^3 = 15\pi \text{ ft}^3
\]
### Final Answer
Thus, the exact volume of the figure is:
\[
\boxed{15\pi} \text{ ft}^3
\]
If further specifications or corrections to the assumptions about dimensions are necessary, please provide those details!
1. The height of the cylinder (h_cyl) is given as 5 ft.
2. The radius of the circular base of both the cylinder and the cone (r) is given as half of the diameter. Since you stated there is a measurement of 3 ft at the end of a line going to the right, I'll assume this is the diameter of the circular base, so the radius \( r = \frac{3 \text{ ft}}{2} = 1.5 \text{ ft} \).
3. The height of the cone (h_cone) is not explicitly given, but letβs assume it to be the same as the height of the cylinder, which is 5 ft for this calculation.
### Volume of the Cylinder
The volume \( V_{cyl} \) of a cylinder is given by the formula:
\[
V_{cyl} = \pi r^2 h_{cyl}
\]
Substituting the values:
\[
V_{cyl} = \pi (1.5 \text{ ft})^2 (5 \text{ ft}) = \pi (2.25 \text{ ft}^2)(5 \text{ ft}) = 11.25\pi \text{ ft}^3
\]
### Volume of the Cone
The volume \( V_{cone} \) of a cone is given by the formula:
\[
V_{cone} = \frac{1}{3} \pi r^2 h_{cone}
\]
Substituting the values:
\[
V_{cone} = \frac{1}{3} \pi (1.5 \text{ ft})^2 (5 \text{ ft}) = \frac{1}{3}\pi (2.25 \text{ ft}^2)(5 \text{ ft}) = \frac{11.25\pi}{3} \text{ ft}^3 = 3.75\pi \text{ ft}^3
\]
### Total Volume of the Figure
To find the total volume \( V_{total} \) of the figure, we add the volumes of the cylinder and the cone:
\[
V_{total} = V_{cyl} + V_{cone} = 11.25\pi \text{ ft}^3 + 3.75\pi \text{ ft}^3 = 15\pi \text{ ft}^3
\]
### Final Answer
Thus, the exact volume of the figure is:
\[
\boxed{15\pi} \text{ ft}^3
\]
If further specifications or corrections to the assumptions about dimensions are necessary, please provide those details!