The document discusses measurements, area, right prisms and cylinders, surface area and volume of prisms and cylinders, pyramids, cones and spheres, and how multiplying dimensions by a factor affects surface area and volume. It provides formulas for calculating surface area and volume of various 3D shapes and explains that multiplying the length, breadth, and height by a factor k will result in the surface area being multiplied by k^2 and volume being multiplied by k^3.

1. 1
Everything Maths www.everythingmaths.co.za
13. Measurements
Grade 10

2. 2
Everything Maths www.everythingmaths.co.za
Area
Area is the two dimensional space inside the boundary of a flat object. It is measured in
square units.

3. 3
Everything Maths www.everythingmaths.co.za
Area contd...

4. 4
Everything Maths www.everythingmaths.co.za
Right prisms and cylinders
A right prism is a geometric solid that has a polygon as it's base and vertical sides
perpendicular to the base. The base and top surface are the same shape and size. It is
called a 'right' prism because the angles between the base and sides are right angles.

5. 5
Everything Maths www.everythingmaths.co.za
Surface area of prisms and cylinders
Surface area is the total area of the exposed or outer surfaces of a prism.
To find the surface area of a prism or cylinder we can unfold the shape into a net:

6. 6
Everything Maths www.everythingmaths.co.za
Volume of prisms and cylinders
Volume is the three dimensional space occupied by an object, or the contents of an object.
It is measured in cubic units.

7. 7
Everything Maths www.everythingmaths.co.za
Pyramids, right cones and spheres
A pyramid is a geometric solid that has a polygon as its base and sides that converge at a
point called the apex. The sides are not perpendicular to the base.

8. 8
Everything Maths www.everythingmaths.co.za
Surface area for square and rectangular prisms

9. 9
Everything Maths www.everythingmaths.co.za
Surface area for right cone and sphere

10. 10
Everything Maths www.everythingmaths.co.za
Volume for square and rectangular prisms

11. 11
Everything Maths www.everythingmaths.co.za
Volume for right cone and sphere

12. 12
Everything Maths www.everythingmaths.co.za
The effect of multiplying by a factor of k
Multiplying one or more dimensions of a prism or cylinder by a constant k affects the surface
area and volume of the object.
V k=kl×kb×kh
=k3
(lbh)
=k3
V
Ak=2[(kl×kh)+(kl×kb)+(kb×kh)]
=k
2
×2(lh+lb+bh)
=k2
A

13. 13
Everything Maths www.everythingmaths.co.za
For more practice see: www.everythingmaths.co.za