Define the term prism .

A prism is a 3D shape with a constant cross-section . It has two identical base shapes connected by parallel edges .

Define the term right pyramid .

A right pyramid is a pyramid where the apex is vertically above the centre of the base.

Define the term right cone .

A right cone is a cone where the apex is vertically above the centre of the base.

How is the formula for the total surface area of a cylinder different to the formula for the curved surface area ?

The formula for the total surface area of a cylinder is different to the formula for the curved surface area as it includes the two end circular faces .

True or False? The surface area of prisms and pyramids with polygon bases is found by adding up the areas of flat faces only.

True. The surface area of prisms and pyramids with polygon bases is found by adding up the areas of flat faces only.

IBMathsDPApplications & Interpretation (AI)HLFlashcards3. Geometry & TrigonometryGeometry of 3D Shapes

Geometry of 3D Shapes (DP IB Applications & Interpretation (AI))

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Front3D Coordinate Geometry
What do the $x$ and $y$ axes typically represent in a 3D Cartesian system?

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What do the $x$ and $y$ axes typically represent in a 3D Cartesian system?
In a 3D Cartesian system, the $x$ and $y$ axes typically represent lateral space (length and width).
What does the $z$ -axis typically represent in a 3D Cartesian system?
In a 3D Cartesian system, the $z$ -axis typically represents vertical height.
State the expression for the midpoint of two points, $(x_{1}, y_{1}, z_{1})$ and $(x_{2}, y_{2}, z_{2})$ in 3D.
The expression for the midpoint of two points, $(x_{1}, y_{1}, z_{1})$ and $(x_{2}, y_{2}, z_{2})$ in 3D is $(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2}, \frac{z_{1} + z_{2}}{2})$
This is given in your exam formula booklet.
What is the formula for finding the distance between two points $(x_{1}, y_{1}, z_{1})$ and $(x_{2}, y_{2}, z_{2})$ in 3D?
The distance between two points is calculated using the formula, $d = \sqrt{{(x_{1} - x_{2})}^{2} + {(y_{1} - y_{2})}^{2} + {(z_{1} - z_{2})}^{2}}$
Where:
- $d$ is the distance between two points
- $(x_{1}, y_{1}, z_{1})$ is the set of coordinates for a known point
- $(x_{2}, y_{2}, z_{2})$ is the set of coordinates for another known point
This is given in your exam formula booklet.
Define the term prism.
A prism is a 3D shape with a constant cross-section.
It has two identical base shapes connected by parallel edges.
State the formula for the volume of a prism.
The formula for the volume of a prism is $V = A h$
Where:
- $V$ is the volume of the prism
- $A$ is the area of the cross-section
- $h$ is the height of the prism
This is given in your exam formula booklet.
What is the formula for the volume of a cuboid?
The formula for the volume of a cuboid is $V = l w h$
Where:
- $V$ is the volume of the cuboid
- $l$ is the length of the cuboid
- $w$ is the width of the cuboid
- $h$ is the height of the cuboid
This is given in your exam formula booklet.
What is the formula for the volume of a cylinder?
The formula for the volume of a cylinder is $V = π r^{2} h$
Where:
- $V$ is the volume of the cylinder
- $r$ is the radius of the circular base of the cylinder
- $h$ is the height of the cylinder
This is given in your exam formula booklet.
Define the term right pyramid.
A right pyramid is a pyramid where the apex is vertically above the centre of the base.
Define the term right cone.
A right cone is a cone where the apex is vertically above the centre of the base.
True or False?
The slant height of a cone is the same as its vertical height.
False.
The slant height of a cone is not the same as its vertical height.
The slant height, $l$ , of a cone is the hypotenuse of the right triangle formed by the radius, vertical height and slant height of the cone.
What is the formula for the volume of a right cone?
The formula for the volume of a right cone is $V = \frac{1}{3} π r^{2} h$
Where:
- $V$ is the volume of the cone
- $r$ is the radius of the circular base of the cone
- $h$ is the vertical (perpendicular) height of the cone
This is given in your exam formula booklet.
What is the formula for the volume of a right pyramid?
The formula for the volume of a right pyramid is $V = \frac{1}{3} A h$
Where:
- $V$ is the volume of the pyramid
- $A$ is the area of the base of the pyramid
- $h$ is the vertical (perpendicular) height of the pyramid
This is given in your exam formula booklet.
What is the formula for the volume of a sphere?
The formula for the volume of a sphere is $V = \frac{4}{3} π r^{3}$
Where:
- $V$ is the volume of the sphere
- $r$ is the radius of the sphere
This is given in your exam formula booklet.
What is the formula for the curved surface area of a cylinder?
The formula for the curved surface area of a cylinder is $A = 2 π r h$
Where:
- $A$ is the curved surface area of the cylinder
- $r$ is the radius of the cylinder
- $h$ is the height of the cylinder
This is given in your exam formula booklet.
How is the formula for the total surface area of a cylinder different to the formula for the curved surface area?
The formula for the total surface area of a cylinder is different to the formula for the curved surface area as it includes the two end circular faces.
State the formula for the total surface area of a cone.
The formula for the total surface area of a cone is $A = π r^{2} + π r l$
Where:
- $A$ is the total surface area of the cone
- $r$ is the radius of the circular base of the cone
- $l$ is the slant height of the cone
This is not given in the exam formula booklet, however the curved surface area of a cone ( $π r l$ ) and the area of a circle ( $π r^{2}$ ) are.
What is the formula for the surface area of a sphere?
The formula for the surface area of a sphere is $A = 4 π r^{2}$
Where:
- $A$ is the surface area of the sphere
- $r$ is the radius of the sphere
This is given in your exam formula booklet.
True or False?
The surface area of prisms and pyramids with polygon bases is found by adding up the areas of flat faces only.
True.
The surface area of prisms and pyramids with polygon bases is found by adding up the areas of flat faces only.

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