can anyone help me please (1 Viewer)

[sanshi]

hi:wave:
im stuck on the following questions and was wondering if anyone coukd help me..

a) A rectangle is cut from a circular disc of radius 6cm. find the area of the largest rectangle that can be produced

b) a surfboard is in the shape of a rectangle and a semi circle. The perimeter is to be 4m. find the maximum area of the surfboard

c) the sum of the dimensions of a box eith a square base is 60 cm. find the dimensions that will give the box a maximum value


thanks heaps....

 

[Mountain.Dew]

hi:wave:
im stuck on the following questions and was wondering if anyone coukd help me..

a) A rectangle is cut from a circular disc of radius 6cm. find the area of the largest rectangle that can be produced

b) a surfboard is in the shape of a rectangle and a semi circle. The perimeter is to be 4m. find the maximum area of the surfboard

c) the sum of the dimensions of a box eith a square base is 60 cm. find the dimensions that will give the box a maximum value

thanks heaps....

okay, for these questions, it will involve more than one variable, perhaps involving height and width, so u must find a a link between those two variables to so that u can eliminate one variable in order to do max - min calculus stuff to get ur answer.

for a) --> u know what the area of a rectangle is width X height. for ease, we use A = w * h

when we draw the rectangle in the circle, realise that when u draw a diagonal to make two triangles, realise that both triangles are right-angled, and u just happen to know the hypotenuse IS the perimeter of the circle. HAHA ==> Pythagora's Theroem.

so, we know that w^2 + h^2 = (12)^2 = 144. THERE IS THE LINK

So, h = sqrt(144 - w^2) ==> sub that into A = w * h, and you get:

A = w * sqrt(144 - w^2) <==here is the equation you use to do max-min calculus to find the width of the rectangle that will give the greatest area. THEN, sub the value of w back into the LINK to find h, then u know the largest area for the rectangle is.

use the same principle applied here to do questions (b) and (c).

if still stuck, im sure other BOS members would be more than happy to assist you.