Cross Sections, Area
If you cut a cylinder horizontally (parallel to the base), what 2D shape is formed?
Circle
If you double all side lengths of a cube, the volume increases by this factor.
What is 8? (2^3=8)
The equations for finding the volume of a prism
V= Area of Base(b)*Height(h)
A vertical slice (perpendicular to the base) through the apex of a cone creates this shape.
Triangle
If you triple all side lengths of a sphere, the surface area increases by this factor.
What is 9? (3^2=9)
The formula for finding the volume of a cylinder
V = pi r^2h
A horizontal slice of a rectangular pyramid creates this shape
What is a rectangle
If two similar solids have a scale factor of (1:4), this is the ratio of their surface areas.
What is (1:16)? (1^2:4^2)
A box has a length of 15 cm, width of 5, and height of 8 cm. What is the volume?
15*5*8= 600^3
This is the maximum number of sides a cross section of a cube can have.
What is six.
If two similar solids have a scale factor of (2:3), this is the ratio of their volumes.
What is (8:27)? (2^3:3^3)
A triangular prism has a base area of 12 cm^2 and a height of 7 cm. What is the volume?
12*7=84^3
If a plane passes exactly through the vertex of a cone, it produces these "degenerate" conic sections.
What are a point, a line, or two intersecting lines?
If you double the size of an animal, this happens to its skin area compared to its weight.
What is it becomes half as much
What is the volume of a cylinder with a diameter of 20 cm and a height of 5 cm?
r = 10cm. V = pi*10^2*5 = 500pi cm^3