Podcast
Questions and Answers
What is the formula to calculate the lateral area of a regular pentagonal prism?
What is the formula to calculate the lateral area of a regular pentagonal prism?
- $L = a * p$, where $a$ is the apothem, and $p$ is the perimeter
- $L = P * h$, where $P$ is the perimeter of the base, and $h$ is the height (correct)
- $L = (1/2) * P * h$, where $P$ is the perimeter of the base, and $h$ is the height
- $L = 2 * P *h$, where $P$ is the perimeter of the base, and $h$ is the height
The formula for the surface area of a cylinder is $SA = 2Ï€r^2 + 2Ï€rh$, where $r$ is the radius, and $h$ is the height. If the radius is doubled, the surface area will always double as well, assuming the height remains constant.
The formula for the surface area of a cylinder is $SA = 2Ï€r^2 + 2Ï€rh$, where $r$ is the radius, and $h$ is the height. If the radius is doubled, the surface area will always double as well, assuming the height remains constant.
False (B)
Describe the key difference between finding the lateral area and the total surface area of a 3D geometric shape.
Describe the key difference between finding the lateral area and the total surface area of a 3D geometric shape.
Lateral area only includes the area of the sides, while the total surface area includes the area of the sides plus the area of the bases.
To find the volume of a pyramid, you multiply the area of the base by the _______ and then multiply by $1/3$.
To find the volume of a pyramid, you multiply the area of the base by the _______ and then multiply by $1/3$.
Match the following terms with their corresponding formulas for a cylinder:
Match the following terms with their corresponding formulas for a cylinder:
What effect does doubling the height of a rectangular prism have on its volume?
What effect does doubling the height of a rectangular prism have on its volume?
If two spheres have the same volume, they must have the same surface area.
If two spheres have the same volume, they must have the same surface area.
Explain how to find the surface area of a cube, given the length of one of its sides.
Explain how to find the surface area of a cube, given the length of one of its sides.
In spherical geometry, lines are defined as __________, and they always intersect.
In spherical geometry, lines are defined as __________, and they always intersect.
Match each 3D shape with its formula for volume:
Match each 3D shape with its formula for volume:
What happens to the volume of a cone if both its radius and height are doubled?
What happens to the volume of a cone if both its radius and height are doubled?
Two cylinders with the same surface area must have the same volume.
Two cylinders with the same surface area must have the same volume.
Explain why doubling the radius of a sphere has a greater impact on its volume than doubling its radius has on its surface area.
Explain why doubling the radius of a sphere has a greater impact on its volume than doubling its radius has on its surface area.
The formula for calculating the volume of a regular hexagonal pyramid is $V = (1/3) * B * h$, where B is the area of the ________ and h is the height of the pyramid.
The formula for calculating the volume of a regular hexagonal pyramid is $V = (1/3) * B * h$, where B is the area of the ________ and h is the height of the pyramid.
Match the term to it's equation:
Match the term to it's equation:
How does the surface area of the larger prism compare to the smaller prism if the ratio of their heights is 2:7 and the surface area of the smaller prism is 50 square meters?
How does the surface area of the larger prism compare to the smaller prism if the ratio of their heights is 2:7 and the surface area of the smaller prism is 50 square meters?
If parallel lines do not exist in spherical geometry, then two lines drawn on a sphere will never intersect.
If parallel lines do not exist in spherical geometry, then two lines drawn on a sphere will never intersect.
What is a horizontal cross section of a solid?
What is a horizontal cross section of a solid?
To determine if two cylinders are congruent, the ______ and ________ must be equal.
To determine if two cylinders are congruent, the ______ and ________ must be equal.
Match each element with the purpose when calculating surface area of a three-dimensional object:
Match each element with the purpose when calculating surface area of a three-dimensional object:
Flashcards
Surface Area
Surface Area
The sum of the areas of all the faces (surfaces) of a 3D solid.
Lateral Area of a Prism
Lateral Area of a Prism
The area of the faces of a prism excluding the bases
Regular Pentagonal Prism
Regular Pentagonal Prism
A prism with bases that are regular pentagons.
Cylinder
Cylinder
Signup and view all the flashcards
Lateral Area of a Cylinder
Lateral Area of a Cylinder
Signup and view all the flashcards
Volume
Volume
Signup and view all the flashcards
Pyramid
Pyramid
Signup and view all the flashcards
Apothem
Apothem
Signup and view all the flashcards
Oblique Cone
Oblique Cone
Signup and view all the flashcards
Hemisphere
Hemisphere
Signup and view all the flashcards
Sphere
Sphere
Signup and view all the flashcards
Lines in Spherical Geometry
Lines in Spherical Geometry
Signup and view all the flashcards
Congruent
Congruent
Signup and view all the flashcards
Similar
Similar
Signup and view all the flashcards
Study Notes
Extending Surface Area & Volume -- Chapter 12
- Front view of a figure from a corner view: See answer key.
- Back view of a figure from a corner view: See answer key.
- Faces of the solid: PQRS, PQT, QTR, RTS, PTS
- Edges of the solid: GJ, HJ, IJ, GH, HI, GI
- Horizontal cross section of the solid: See answer key
- Horizontal cross section of the solid: See answer key.
- Lateral area of a triangular prism of height 8 cm, with base sides 4 cm, 5 cm, and 6 cm: 120 cm²
- Surface area of a solid with sides of 1 in: 6 in²
- Surface area of a prism with sides of 6 ft, 5 ft, and 9 ft: 258 ft²
- Lateral area of a regular pentagonal prism if the base perimeter is 50 inches, and the height is 15 inches: 750 in²
- Lateral area of a right cylinder with a diameter of 8.6 yards and a height of 19.4 yards: 524.1 yd²
- Lateral area of a right cylinder with a diameter of 23.6 meters and a height of 11.4 meters: 845.2 m²
- The radius of a cylinder with a surface area of 180 square inches and a height of 9 inches: 6 in.
- The radius of a right cylinder with a surface area of 252 square feet and a height of 11 feet: 7 ft
- Lateral area of a regular hexagonal pyramid with base edges of 10 inches and a slant height of 9 inches: 270 in²
- Surface area of a regular hexagonal pyramid with base edges of 10 inches and a slant height of 9 inches: 270 + 150√3 in²
- Lateral area of a regular octagonal pyramid, with base edges 9 feet long, a slant height of 15 feet, and a base with an apothem of 10.86 feet: 540 ft²
- Surface area to the nearest tenth, of a regular octagonal pyramid, with base edges 9 feet long, a slant height of 15 feet, and a base with an apothem of 10.86 feet: 931.0 ft²
- Lateral area of a right circular cone with a radius of 4 feet and a height of 3 feet: 62.8 ft²
- Surface area of a right circular cone with a radius of 4 feet and a height of 3 feet: 113.1 ft²
- Lateral area of a cone with a radius of 5 centimeters and a height of 12 centimeters: 204.2 cm²
- Surface area of a cone with a radius of 5 centimeters and a height of 12 centimeters: 282.7 cm²
- Length of a lateral edge of a rectangular prism with a volume of 120 cubic feet and a base area of 60 square feet: 2 ft
- Volume of the water in an aquarium 18 inches long, 8 inches wide, and 14 inches high, filled to a depth of 4 inches: 576 in³
- Volume of a cylinder with a 12-foot radius and a 17-foot height: 7690.6 ft²
- Volume of the cylinder: 923.6 cm³
- Volume of a regular hexagonal pyramid with a height of 15 feet and a base 6 feet on each side: 467.7 ft³
- The volume of a square pyramid having a height of 51 inches and a base with 11-inch sides is 2057 in³
- Volume of the oblique cone: 103.2 ft³
- Volume of an oblique cone: 100.5 cm³
- Surface area of a hemisphere: 1140.4 cm²
- Volume of the sphere: 208.8 in³
- Volume of a sphere: 106.4 cm³
- A line in spherical geometry is best described as a great circle.
- Parallel lines do not exist in spherical geometry because lines in spherical geometry are great circles that always intersect.
- The two cylinders provided are neither congruent nor similar.
- The two cubes provided are similar.
- The surface area of the larger prism: 612.5 m²
- Volume of the larger pyramid: 1562.5 ft³
- The surface area of a sphere inscribed in a cube with sides of 6 inches: 113.1 in²
- The surface area of a sphere inscribed in a cube with sides of 8 inches: 201.1 in²
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
