Liz has moved into a new flat. She wants to have these 3 walls of the bedroom painted.
5 m
5 m
4m
Diagrams not
accurately drawn
wall
3 m
wall
3 m
wall
3 m
Liz has 3 tins of paint.
1 tin of paint covers 13 m².
(a) Does Liz have enough paint to cover the 3 walls?
Show why you think this.
Use the space below to show clearly how you get your answer.

Yes. She has enough paint.

Step-by-step explanation:

Her walls combined are approximately 100m

and 1 tin covers 169m of a wall because 13 × 13 is 169.

but she only needs 100, so she will have enough.

the remaining amount of pains she has left is 407 because she still has two time left.

two tins of paint = 338m of paint used on walls then add the remaining from the used Tim which is 69. That'll be 407.

I hope you understand

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.