SOLUTION: A cuboid of volume 1125cm^3 has length equal to three times the breadth.
(A)- show that the surface area of the cuboid may be expressed as 6x^2+3000/x
(B) - find the dimensio
Algebra.Com
Question 484458: A cuboid of volume 1125cm^3 has length equal to three times the breadth.
(A)- show that the surface area of the cuboid may be expressed as 6x^2+3000/x
(B) - find the dimensions of the cuboid that give the minimum surface area.
I think i have a right, just need to check but i am completely stuck on b, help would be much appreciated.
the breadth is x and the length is 3x.
thanks
Answer by chessace(471) (Show Source): You can put this solution on YOUR website!
Yes, you are on the right track.
You have surface area as f(x), so to find the min,
differentiate and set to 0.
12x-3000x^-2 = 0
*(1/12)x^2: x^3 - 250 = 0
breath x = 5 cubeRoot(2) cm
L = 15 cubeRoot(2) cm
H = 15/cubeRoot(4) cm
Double check and the product is indeed 1125 cm^3
RELATED QUESTIONS
" A cuboid of volume 1125cm^3 has length equal to three times the breadth.
(a) Show... (answered by ewatrrr)
the sum of length, breadth and depth of a cuboid is 19 cm and the length of diagonal is... (answered by ikleyn,Alan3354,KMST)
A cuboid has a rectangular front face with an are a of 47cm square an a ratio of the... (answered by Alan3354)
The cuboid has a width of 5cm and a length of 10cm and the surface area of 280cm² what is (answered by KMST)
A cuboid has a pair of square faces,with edge lengths p cm. The total volume of the... (answered by KMST)
The surface area and diagonal of a cuboid are 288 sq.cm and 12 cm respectively. Show that (answered by ankor@dixie-net.com,ikleyn)
the ratio height: length: depth of this cuboid is 2:3:4
the total surface area is... (answered by phillywily)
A cuboid has a volume of 2430cm3, it's height is 10cm and the width is 1/3 of the length... (answered by Alpha Maximus)
A cuboid has a rectangular front face with an area of 47cm squared. If the side grace is... (answered by Alan3354)