Core Chapter 6: Measurement

Question 1

State and apply for the formulas for area and circumference of a circle

Answer 1

Circumference = 2πr
Area = π(r)²

Question 2

Define an arc and find arc length
(when θ is in both degree and radian)

Answer 2

Arc: Part of circle joining 2 points subtended by θ

Arc length (when θ is in deg)
= θ/360 x 2πr

Arc length (l) (when θ is in rad)
= rθ

Question 3

Define a sector and find area and perimeter of a sector

Answer 3

Sector: Region between 2 radii and an arc

Perimeter = 2r + rθ [rad] OR 2r +θ/360 x 2πr [deg]

Area = 1/2 (r²θ) [rad] OR θ/360 x πr² [deg]

Question 4

Find the surface area of both solids with plane surfaces and solids with curved surfaces

Answer 4

Surface area of solids with plane faces: sum of the area of all the faces of a solid (area of the net)

Solids with curved faces: cylinder, sphere and cone
- Surface area of a cylinder = 2πrh (area of the curved surface) + 2πr² (area of the 2 circular bases)
- Surface area of a sphere = 4πr²
- Surface area of a cone = πrs (area of the curved surface) + πr² (area of the circular base)

Question 5

Find the volume of both solids with uniform cross-section and tapered solids

Answer 5

Volume of solids with uniform cross section: area of base x height
- Eg. Volume of cylinder = πr²(volume of base) x h (height)

Volume of tapered solids: 1/3 x (area of base x height)
- Eg. Volume of sphere = 4/3πr³