Question

A cone has a radius of 4.96cm and a volume of 102cm. Work out an estimate for the height of the cone. You must show your working.

So stuck, I keep getting 3.9 but apparently its wrong.

Answer 1

Cone height formula:

H = volume x 3 / pi x radius squared

H = 102 x 3 / pi x 4.96 sqrd

H = 306 / pi x 24.6

H = 3.9612 ≈ 4


Maybe you are asked for the height rounded to 1 decimal, and rounded, it would be Height = 4

Answer 2

3.96 cm

The formula for the volume of a cone is:

V = (1/3)πr^2 x h

Where V is the volume, π is approximately 3.14, r is the radius, and h is the height of the cone.

We know that the volume of the cone is 102 cm^3 and the radius of the cone is 4.96 cm. So we can substitute these values into the formula:

102 = (1/3)π(4.96)^2 x h

To estimate height of the cone we need to divide both sides of the equation by (1/3)π(4.96)^2.

h = 3.959207...

So, the height of the cone is approximately 3.96 cm.