Key Terms
Volume of Prisms
Surface Area of Prisms
The volume of Cones, Cylinders, and Spheres
Surprise Challenge
100
What is a rectangular prism?
A rectangular prism is a three-dimensional shape with a top and bottom (base) that are congruent rectangles and lateral (side) faces that are parallelograms.
100
The prism is cut vertically into two smaller triangular prisms. How does the volume of each smaller prism compare to the original prism?
Each smaller prism will have half the volume of the original prism.
100
The total surface area of any prism includes the lateral surface area and the base area. (True or False)
True
100
A cone has the same radius and height as a cylinder. What is the ratio of the volume of the cylinder to the volume of the cone?
The ratio is 3:1
(since the volume of a cone is one-third the volume of a cylinder with the same base and height).
100
Name three things from your life that are shaped like a cone, a sphere, and a cylinder?
(answers may vary)
Cone: Ice cream cone
Sphere: Basketball
Cylinder: Water bottle
200
What is a net of a 3D shape?
A two-dimensional pattern that can be folded into a three-dimensional figure.
200
Find the volume of a rectangular prism with a base of 3 cm x 4 cm and a height of 5 cm.
60 cm³
200
A rectangular prism has a length of 8 cm, a width of 5 cm, and a height of 3 cm. Calculate the surface area of the prism.
158 cm²
200
A cone has a radius of 5 cm and a height of 12 cm. What is its volume?
314 cm³
200
Name three everyday objects that can be both filled and wrapped.
(answers may vary)
Burrito: Can be filled with ingredients and wrapped in a tortilla.
Gift box: Can be filled with a present and wrapped with gift paper.
Water bottle: Can be filled with water and wrapped in a protective sleeve or bag.
300
What is a cylinder?
A cylinder is a three-dimensional geometric shape with two parallel, identical circular bases that are connected by a curved surface.
300
What is the volume of this prism?
36 in³
300
Can two prisms have different volumes but the same surface areas?
Yes, two prisms can have different volumes but the same surface area.
Prism 1:
Length: 4 units, Width: 2 units, Height: 6 units
Surface area = 88 square units
Prism 2:
Length: 3 units, Width: 4 units, Height: 32/7 units
Surface area = 88 square units
300
A sphere has a radius of 5 cm. What is its volume?
523.33 cm³
300
What two-dimensional shapes appear if you slice a cone as shown on each figure?
Triangle (left),
Trapezoid (middle), and
Circle (right)
400
What is the difference between surface area and volume?
Surface Area is the total area of all the faces or outer surfaces of a 3D object. It measures how much material would be needed to cover the outside of the object.
Volume: This is the amount of space inside a 3D object. It measures how much space the object occupies or can hold.
400
Suppose that a square prism has a base with sides of 3 cm and a volume of 81cm³.
What is the height of the prism?
9 cm
400
Which of the following are true in the case of a prism? (May have multiple answers)
A. A prism is a 3-dimensional solid object.
B. It has identical ends (polygonal) and flat faces.
C. Surface area of a Prism= 2 × (Base Area) + (Lateral surface area)
All of them.
(A, B, and C)
400
A cylinder is filled with water and has a height of 20 cm and a radius of 5 cm. If a solid sphere of radius 5 cm is dropped into the cylinder, how much will the water level rise?
(round to the nearest hundredth)
6.67 cm
400
If you could fill and wrap anything in the world, what would it be and why? Get creative with your answer!
Sounds creative!
500
What is the definition of pi (π)?
pi (π) The mathematical name for the ratio of a circle's circumference to its diameter. This ratio is the same for every circle, approximately equal to 3.1415926.
500
A right prism has a volume of 1,000 cm³ and a base area of 50 cm².
If the height is increased by 2 cm and the base area is modified such that it increases by 20%, calculate the new volume of the prism.
1320 cm³
500
For a rectangular prism, if the length, width, and height are all odd numbers, the surface area always be an even number. (Yes/No)
Why or why not?
Yes, the surface area of a rectangular prism must be an even number if the length, width, and height are all odd. This is because the surface area formula involves multiplying by 2, which ensures the result will be even.
500
A composite shape is made by attaching a hemisphere on top of a cylinder. The cylinder has a radius of 4 cm and a height of 8 cm. The hemisphere shares the same radius. What is the total volume of the composite shape?
535.89 cm³
500
If the Earth could be 'filled' with something and 'wrapped' in something for a day, what would you choose and why?
Sounds creative!