Volume of Spheres
What is the formula for the volume of a sphere?
V=4/3 π r3
What is the formula for the volume of a cylinder?
V=π r2
What is the formula for the volume of a cone?
V=1/3 π r2 h
What is the formula for the lateral surface area of a prism?
Lateral Area=P×h (Perimeter of the base × height)
What is the formula for the lateral surface area of a cylinder?
LA=2 π r h
A sphere has a radius of 5 cm. What is its volume?
V≈523.6 cm3
A cylinder has a radius of 4 cm and height of 10 cm. What is its volume? (Round to the nearest tenth.)
502.7 cm³
A cone has a radius of 3 cm and a height of 9 cm. What is its volume? (Round to the nearest tenth.)
84.8 cm³
What is the formula for the total surface area of a rectangular prism?
SA= Ph+ 2B
P= Perimeter of Base
h = height
B = Area of Base
What is the formula for the total surface area of a cylinder?
SA=2πrh+2πr2
If the diameter of a sphere doubles, by what factor does the volume increase?
8 times larger
If the radius of a cylinder doubles while keeping the height the same, by what factor does the volume increase?
4 times larger
If the height of a cone is tripled while keeping the same radius, how does the volume change?
The volume triples.
A rectangular prism has a length of 4 cm, width of 3 cm, and height of 5 cm. What is its total surface area?
A: 94 cm²
A cylinder has a radius of 3 cm and height of 8 cm. What is its lateral surface area?
150.8 cm²
A sphere has the same volume as a cylinder with height equal to the sphere’s diameter. What is the relationship between their radii?
The sphere's radius is the same as the cylinder's radius.
A cylinder has a volume of 1,570 cm³ and a height of 10 cm. What is its radius? (Use π ≈ 3.14, round to nearest tenth.)
r ≈ 7 cm
A cone has a volume of 150 cm³ and a height of 10 cm. What is its radius? (Use π ≈ 3.14, round to nearest tenth.)
r ≈ 4.8 cm
A triangular prism has a triangular base with sides 6 cm, 8 cm, and 10 cm, and a height of 12 cm. Find the lateral surface area.
288 cm²
If a cylinder has a total surface area of 314 cm² and a height of 10 cm, what is its radius? (Round to nearest tenth.)
r ≈ 5 cm
If a sphere has a volume of 904.32 cm³, what is its radius? (Use π ≈ 3.14, round to nearest tenth.)
r ≈ 6 cm
A cylinder and a cone have the same height and radius. What is the ratio of their volumes?
The volume of the cylinder is 3 times the volume of the cone.
A cone and a sphere have the same radius, and the cone's height is twice the sphere's radius. What is the ratio of their volumes?
The sphere's volume is twice the cone's volume.
A cube has a total surface area of 216 cm². What is its edge length?
A: 6 cm
A metal pipe is in the shape of a hollow cylinder with an outer radius of 10 cm, an inner radius of 8 cm, and a height of 15 cm. What is the lateral surface area of the pipe?
1,696.5 cm²