The height of the right circular cone is given as 15 centimeters. Therefore, the correct answer is:
15 cm.
Use the image to answer the question
A cone is marked with a height of 15 centimeters and a diameter of 16 centimeters, both shown as perpendicular dotted lines. The slant height is 17 centimeters.
what is the height of the right circular cone?
17 cm
16 cm
8 cm
15 cm
9 answers
use the image to answer the question
An oblique cylinder is labeled with a height of 15 centimeters and radius 5 centimeters.
find the volume of the cylinder below. Use the approximation 3.14 for pi.
235.5 cubic centimeters
1177.5 centimeters
1177.5 cubic centimeters
471 square centimeters
An oblique cylinder is labeled with a height of 15 centimeters and radius 5 centimeters.
find the volume of the cylinder below. Use the approximation 3.14 for pi.
235.5 cubic centimeters
1177.5 centimeters
1177.5 cubic centimeters
471 square centimeters
To find the volume \( V \) of a cylinder, you can use the formula:
\[ V = \pi r^2 h \]
where:
- \( r \) is the radius,
- \( h \) is the height, and
- \( \pi \) is approximately 3.14.
Given:
- Height \( h = 15 \) cm
- Radius \( r = 5 \) cm
Now, substituting the values into the formula:
\[ V = 3.14 \times (5)^2 \times 15 \] \[ V = 3.14 \times 25 \times 15 \] \[ V = 3.14 \times 375 \] \[ V = 1177.5 \text{ cubic centimeters} \]
Thus, the volume of the cylinder is 1177.5 cubic centimeters.
Adrian is painting the outside of a cylinder that he plans to use as a coffee table. The cylinder has a radius of 4 feet and a height of 3 feet. Adrian wants to paint all around the outside of the cylinder, including the top and bottom faces. In order to understand how much paint is needed, he wants to know the surface are of the outside of the cylinder. What is the surface area of the cylinder, measured in square feet? Use 3.14 for pi and round your answer to the nearest tenth.
___ ft^2
___ ft^2
To find the surface area of a cylinder, we can use the formula:
\[ \text{Surface Area} = 2\pi r(h + r) \]
where:
- \( r \) is the radius,
- \( h \) is the height,
- \( \pi \) is approximately 3.14.
Given:
- Radius \( r = 4 \) feet
- Height \( h = 3 \) feet
Now, substituting the values into the formula:
\[ \text{Surface Area} = 2 \times 3.14 \times 4 \times (3 + 4) \]
Calculating:
- Calculate \( h + r = 3 + 4 = 7 \)
- Now substitute:
\[ \text{Surface Area} = 2 \times 3.14 \times 4 \times 7 \]
Calculating step-by-step:
\[ \text{Surface Area} = 2 \times 3.14 \times 4 \times 7 = 2 \times 3.14 \times 28 \] \[ = 2 \times 87.92 \] \[ = 175.84 \]
Now rounding to the nearest tenth:
\[ \text{Surface Area} \approx 175.8 \text{ ft}^2 \]
Therefore, the surface area of the cylinder is \( \boxed{175.8} \) ft².
Eli is making a model castle out of clay. One of the roof peaks is in the shape of a cone with a diameter of 14 inches and a slant height of 20 inches. What is the surface area of the cone peak? Round your answer to the nearest hundredth. Use 3.14 for pi.
__ square inches
__ square inches
To find the surface area of a cone, you can use the formula:
\[ \text{Surface Area} = \pi r l + \pi r^2 \]
where:
- \( r \) is the radius of the base,
- \( l \) is the slant height, and
- \( \pi \) is approximately 3.14.
Given:
- Diameter = 14 inches, so the radius \( r = \frac{14}{2} = 7 \) inches
- Slant height \( l = 20 \) inches
Now substitute the values into the formula:
- Calculate the lateral surface area:
\[ \text{Lateral Surface Area} = \pi r l = 3.14 \times 7 \times 20 \]
Calculating:
\[ 3.14 \times 7 = 21.98 \] \[ 21.98 \times 20 = 439.6 \]
- Calculate the area of the base:
\[ \text{Base Area} = \pi r^2 = 3.14 \times (7^2) = 3.14 \times 49 \]
Calculating:
\[ 3.14 \times 49 = 153.86 \]
- Now sum the lateral surface area and the base area:
\[ \text{Surface Area} = \text{Lateral Surface Area} + \text{Base Area} = 439.6 + 153.86 \] \[ \text{Surface Area} = 593.46 \]
Now, rounding to the nearest hundredth:
The surface area of the cone peak is \( \boxed{593.46} \) square inches.
A 3 D cylinder shows a base radius of 8 millimeters and perpendicular height of 13 millimeters. A right angle is formed at the center of the base.
find the volume of the cylinder, cubic millimeters. Round your answer to the nearest hundredth
___ cubic millimeters
find the volume of the cylinder, cubic millimeters. Round your answer to the nearest hundredth
___ cubic millimeters
To find the volume \( V \) of a cylinder, you can use the formula:
\[ V = \pi r^2 h \]
where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder, and
- \( \pi \) is approximately 3.14.
Given:
- Base radius \( r = 8 \) millimeters
- Height \( h = 13 \) millimeters
Now substituting the values into the formula:
- Calculate \( r^2 \):
\[ r^2 = 8^2 = 64 \]
- Now substitute into the volume formula:
\[ V = \pi r^2 h = 3.14 \times 64 \times 13 \]
- Calculate \( 64 \times 13 \):
\[ 64 \times 13 = 832 \]
- Now compute the volume:
\[ V = 3.14 \times 832 \]
Calculating:
\[ 3.14 \times 832 = 2616.08 \]
Now rounding to the nearest hundredth:
The volume of the cylinder is \( \boxed{2616.08} \) cubic millimeters.