Pyramids and Prism
What is the formula for finding the volume of a rectangular prism?
V=length×width×height
What is the formula for the volume of a cylinder?
V=π x r2 x h
If a shape is enlarged by a scale factor of 2, how does its area change?
The area becomes 4 times larger because area scales by the square of the scale factor.
Cross Sections & Solids of Rotation
Cross Sections & Solids of Rotation
Explain how do you find the missing angle of a triangle if we know two of them
Subtracting from 180 degrees
What is the key difference between how you calculate the volume of a prism and a pyramid?
A pyramid’s volume is one-third of the volume of a prism with the same base and height
What is the main difference between a cylinder and a cone when calculating volume?
A cone’s volume is one-third of the volume of a cylinder with the same base and height:
If a 3D figure is scaled by a factor of 3, how does the volume change?
The volume becomes 27 times larger because volume scales by the cube of the scale factor.
What shape is the cross section of a cylinder when it is sliced horizontally (parallel to the base)?
A circle
What you would use to find the missing side length of a right triangle if you know two of them
the Pythagorean Theorem? ("a2 + b2 = c2)
A square pyramid has a base side length of 6 meters and a height of 10 meters. What is its volume?
Base area = 6×6=36 m2
Volume = 13×36×10 =120 m3
A cylinder has a radius of 4 cm and a height of 6 cm. What is its volume? (Use 3.14 for pi)
V=π x r2 x h = 3.14×16×6=301.44 cm3
A square has an area of 25 cm². If its side lengths are scaled by a factor of 2, what is the new area?
New area = 25×4=100 cm2
What solid is formed when a rectangle is rotated around one of its shorter sides?
A cylinder
What transformation preserves both angle measures and side lengths?
A rigid transformation (translation, rotation, or reflection)
A square pyramid and a square prism have the same base area of 36 in² and height of 12 in. What’s the difference in their volumes?
Prism: 36×12=432 in3
Pyramid: 1/3×36×12=144 in3
Difference: 432−144 = 288
A cone and a cylinder have the same radius and height. If the cylinder's volume is 150 cm³, what is the cone's volume?
V= 1/3 ×150=50 cm3
A cube has a volume of 64 in³. If the cube is scaled down by a factor of 0.5, what is the new volume?
New volume = 64×(0.5)3=64×0.125=8 in3
What is the shape of the cross section when a cone is sliced vertically through its apex?
A triangle
What is the name of the line that divides a segment into two equal parts at 90 degrees?
A perpendicular bisector
A rectangular pyramid has a volume of 120 m³ and a height of 10 m. What is the area of its base?
Use V = 13 × Base Area × Height
120 =13 × B × 10 ⇒ B=36 m2
A cone has a volume of 84 cm³ and a radius of 3 cm. What is the height? (Use pi = 3.14)
h ≈ 8.92 cm
An object’s surface area increased by a factor of 9. What is the scale factor applied to its side lengths?
The scale factor is 3, since sqrt{9} = 3
A semicircle is rotated around its straight edge. What 3D solid is formed?
A sphere
Two similar triangles have a side length ratio of 3:5. The area of the smaller triangle is 27 cm². What is the area of the larger triangle?
Area ratio = 32:52=9:25
Let the larger area be x:
9/25=27/x ⇒ 9x=675 ⇒ x=75 cm2