Question

Which conical container holds more water?
cone 1
4 cm on base
8 cm on vertical slant height
cone 2
8 cm on vertical slant height
6cm on base
Figure not drawn to scale.

Answer 1

To determine which conical container holds more water, we need to calculate the volume of each cone using the given measurements.

The formula to calculate the volume of a cone is:
V = (1/3) * π * r^2 * h

Let's calculate the volume for each cone:

Cone 1:
We are given that the base has a diameter (and hence, radius) of 4 cm. The vertical slant height is given as 8 cm.

Radius (r) = 4 cm / 2 = 2 cm
Height (h) = 8 cm

V1 = (1/3) * π * 2^2 * 8
V1 = (1/3) * π * 4 * 8
V1 = (4/3) * π * 8
V1 = 32π/3 ≈ 33.51 cm^3 (rounded to two decimal places)

Cone 2:
We are given that the base has a diameter (and hence, radius) of 6 cm. The vertical slant height is given as 8 cm.

Radius (r) = 6 cm / 2 = 3 cm
Height (h) = 8 cm

V2 = (1/3) * π * 3^2 * 8
V2 = (1/3) * π * 9 * 8
V2 = (3/3) * π * 9 * 8
V2 = 24π ≈ 75.40 cm^3 (rounded to two decimal places)

Therefore, Cone 2 holds more water as it has a larger volume compared to Cone 1.