Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
To determine the volume of a cone, we use the formula:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
where:
- [tex]\( V \)[/tex] is the volume of the cone,
- [tex]\( \pi \)[/tex] (pi) is a constant approximately equal to 3.14,
- [tex]\( r \)[/tex] is the radius of the base of the cone, and
- [tex]\( h \)[/tex] is the height of the cone.
Given:
- The height [tex]\( h \)[/tex] of the cone is 19 inches,
- The radius [tex]\( r \)[/tex] of the base is 11 inches,
- We use [tex]\( \pi \approx 3.14 \)[/tex].
Let's plug these values into the formula:
[tex]\[ V = \frac{1}{3} \times 3.14 \times (11)^2 \times 19 \][/tex]
First, calculate [tex]\( r^2 \)[/tex]:
[tex]\[ (11)^2 = 121 \][/tex]
Next, multiply [tex]\( 121 \)[/tex] by the height [tex]\( 19 \)[/tex]:
[tex]\[ 121 \times 19 = 2299 \][/tex]
Now, multiply this result by [tex]\( \pi \)[/tex]:
[tex]\[ 2299 \times 3.14 = 7225.86 \][/tex]
Finally, multiply by [tex]\( \frac{1}{3} \)[/tex]:
[tex]\[ \frac{1}{3} \times 7225.86 = 2406.2866666666664 \][/tex]
Rounding this result to the nearest hundredth:
[tex]\[ V \approx 2406.29 \][/tex]
Thus, the volume of the cone is:
[tex]\[ 2406.29 \, \text{cubic inches} \][/tex]
So, the volume of the cone, rounded to the nearest hundredth, is 2406.29 cubic inches.
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
where:
- [tex]\( V \)[/tex] is the volume of the cone,
- [tex]\( \pi \)[/tex] (pi) is a constant approximately equal to 3.14,
- [tex]\( r \)[/tex] is the radius of the base of the cone, and
- [tex]\( h \)[/tex] is the height of the cone.
Given:
- The height [tex]\( h \)[/tex] of the cone is 19 inches,
- The radius [tex]\( r \)[/tex] of the base is 11 inches,
- We use [tex]\( \pi \approx 3.14 \)[/tex].
Let's plug these values into the formula:
[tex]\[ V = \frac{1}{3} \times 3.14 \times (11)^2 \times 19 \][/tex]
First, calculate [tex]\( r^2 \)[/tex]:
[tex]\[ (11)^2 = 121 \][/tex]
Next, multiply [tex]\( 121 \)[/tex] by the height [tex]\( 19 \)[/tex]:
[tex]\[ 121 \times 19 = 2299 \][/tex]
Now, multiply this result by [tex]\( \pi \)[/tex]:
[tex]\[ 2299 \times 3.14 = 7225.86 \][/tex]
Finally, multiply by [tex]\( \frac{1}{3} \)[/tex]:
[tex]\[ \frac{1}{3} \times 7225.86 = 2406.2866666666664 \][/tex]
Rounding this result to the nearest hundredth:
[tex]\[ V \approx 2406.29 \][/tex]
Thus, the volume of the cone is:
[tex]\[ 2406.29 \, \text{cubic inches} \][/tex]
So, the volume of the cone, rounded to the nearest hundredth, is 2406.29 cubic inches.
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.