The diagram below shows the menu from a fast food restaurant.

1. Calculate the cost if all required items are bought a la carte.

Required items:

• 2 burgers
• 1 medium fries for Bart
• 1 large drink for Albert
• 1 medium drink for Bart

Cost:
$2(\$3.20)+\$2.20+\$3.60+\$2.80=\$15.00$

2. Calculate the cost using one regular Combo A for Bart.

Buy 1 Combo A for Bart:

$\text{Burger + medium fries + medium drink}=\$5.90$

Then buy Albert's burger and large drink a la carte:

$\$5.90+\$3.20+\$3.60=\$12.70$

3. Calculate the cost using two Combo A meals with one upsized.

Buy 2 Combo A meals and upsize one drink and fries to large:

$2(\$5.90)+\$1.10=\$12.90$

This gives both burgers, Bart's medium drink and fries, and Albert's large drink.

4. Compare the three costs and choose the cheapest valid order.

The three costs are:

$\$15.00,\quad \$12.70,\quad \$12.90$

Since
$\$12.70<\$12.90<\$15.00,$
the cheapest option is to buy 1 Combo A for Bart, plus 1 burger and 1 large drink a la carte for Albert.

1. Identify the radii and calculate the common bracketed expression in the volume formula.

Top diameter $=9\text{ cm}$, so $R=4.5\text{ cm}$.

Bottom diameter $=6\text{ cm}$, so $r=3\text{ cm}$.

$R^2+Rr+r^2=4.5^2+(4.5)(3)+3^2$
$=20.25+13.5+9=42.75$

2. Calculate the volume of the medium cup.

For the medium cup, $h=13\text{ cm}$.

$V_M=\frac{1}{3}\pi(13)(42.75)$
$=185.25\pi$
$\approx 582\text{ cm}^3$

3. Calculate the volume of the large cup.

For the large cup, $h=17\text{ cm}$.

$V_L=\frac{1}{3}\pi(17)(42.75)$
$=242.25\pi$
$\approx 761\text{ cm}^3$

4. Compare the value for money using volume per dollar.

From part (a), the drink prices are:

Medium drink: $2.80, Large drink: $3.60.

Medium cup:
$\frac{582}{2.80}\approx 207.9\text{ cm}^3\text{ per dollar}$

Large cup:
$\frac{761}{3.60}\approx 211.4\text{ cm}^3\text{ per dollar}$

Since $211.4>207.9$, the large cup gives more drink per dollar.