Question

george has a conical scoop with height 12 cm and radius 1.5 cm and a cylindrical storage bin with height 24 cm and radius 6 cm. how many scoops of sugar will fit into the storage bin?
a) 16
b) 24
c) 96
d) 144

Explanation:

Step1: Recall volume formulas

The volume of a cylinder is \( V_{cylinder} = \pi r^2 h \), and the volume of a cone is \( V_{cone} = \frac{1}{3}\pi r^2 h \).

Step2: Calculate volume of cylindrical bin

For the cylinder, \( r = 6 \) cm, \( h = 24 \) cm.
\( V_{cylinder} = \pi \times 6^2 \times 24 = \pi \times 36 \times 24 = 864\pi \) \( \text{cm}^3 \).

Step3: Calculate volume of conical scoop

For the cone, \( r = 1.5 \) cm, \( h = 12 \) cm.
\( V_{cone} = \frac{1}{3}\pi \times (1.5)^2 \times 12 = \frac{1}{3}\pi \times 2.25 \times 12 = 9\pi \) \( \text{cm}^3 \).

Step4: Find number of scoops

Divide the volume of the cylinder by the volume of the cone:
\( \text{Number of scoops} = \frac{V_{cylinder}}{V_{cone}} = \frac{864\pi}{9\pi} = 96 \).

Answer:

C) 96