2010 A-level H2 Mathematics (9740) Paper 1 Question 9 Suggested Solutions

By KS Teng

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

Total Volume = 3x(x)y = 300

x^2y = 100

y = \frac{100}{x^2}

Total Surface Area, A = 3x(x) + 8x(y) + 3x(x) + 8x(ky)

= 6x^2 + (k+1) \frac{800}{x}

\frac{dA}{dx} = 12x - (k+1)\frac{800}{x^2} = 0

x^3 = \frac{200}{3} (k+1)

x = ^3 \sqrt{\frac{200}{3}(k+1)}

\frac{d^2A}{dx^2} = 12 + (k+1) \frac{1600}{x^3} = 12 + (k+1)\frac{1600}{\frac{200}{3}(k+1)} = 36 > 0

Thus, x=^3 \sqrt{\frac{200}{3}(k+1)} gives a minimum total surface area.

(ii)
\frac{y}{x} = \frac{100}{x^3} = \frac{3}{2(k+1)}

(iii)
0 \textless k \le 1

1 \textless k+1 \le 2

\frac{1}{2} \le \frac{1}{k+1} \textless 1

\frac{3}{4} \le \frac{3}{2(k+1)} \textless \frac{3}{2}

\frac{3}{4} \le \frac{y}{x} \textless \frac{3}{2}

(iv)
If the box has square ends, then y=x

\frac{3}{2(k+1)} = 1

k = \frac{1}{2}

KS Comments:

Comments
    pingbacks / trackbacks

    Leave a Comment

    Contact Us

    CONTACT US We would love to hear from you. Contact us, or simply hit our personal page for more contact information

    Not readable? Change text. captcha txt
    0

    Start typing and press Enter to search

    2010 A-level H2 Mathematics (9740) Paper 1 Question 8 Suggested SolutionsJC Mathematics
    2010 A-level H2 Mathematics (9740) Paper 1 Question 10 Suggested SolutionsJC Mathematics