Shapes Flashcards
(26 cards)
what is a sector?
a region bounded by an arc and two radii
how do you find the perimeter of a sector?
arc length + 2r
Ө/360 x 2πr + 2r
how do you work out the arc length?
Ө/360 x 2πr
how do you work out the area of a sector?
Ө/360 x πr²
how do you work out the volume of a prism?
area of cross-section x length
how do you work out the volume of a cuboid?
height x width x length
hwl
how do you work out the volume of a triangular prism?
base x height/2 x length
bh/2 x l
how do you work out the volume of a kite prism?
width x height/2 x length
wh/2 x l
how do you work out the volume of a trapezoidal prism?
shorter top side +longer bottom side/2 x height x length
a+b/2 x h x l
how do you work out the volume of a cylinder?
πr² x l
how do you work out the surface area of a closed cylinder?
area of rectangle = length x width (width = circumference of circle)
the width of circumference = πd
the area of the circle = πr²
sa = 2πr² + πd x length
how do you work out the surface area of an open cylinder?
πr² + πd x length
what is the difference between an open and closed cylinder?
open cylinder = one circle
closed cylinder = two circles
what is the curved surface area of a cone?
π x radius x length (slopping height)
πr x l
what is the area of a circle?
πr²
how do you find l (the slopping height)?
pythagoras’ theorum
what is pythagoras’ theorum
a² + b² = c²
what is the surface area of a cone?
πrl + πr²
what is the volume of a cone?
1/3x πr² x height
1/3x πr² x h
what are some pythagorian triples?
3, 4, 5
5, 12, 13
how do you work out the volume of a sphere?
4/3 x πr³
how do you work out the surface area of a sphere?
4πr²
how do you work out the volume of a hemisphere?
2/3 x πr³
how do you work out the surface area of a hemisphere?
3πr²
