Question

Figure 1 shows a paperweight made from a hollow hemisphere and a hollow cone. The paperweight contains sand so that the sand exactly fills the hemisphere. The radius of the hemisphere is equal to the radius of the base of the cone. The height of the cone is 15cm and the volume of the cone is 180π cm3 Figure 2 below shows the paperweight after it has been turned upside down. Diagram NOT accurately drawn h cm Figure 2 The height of the sand in the cone is h cm. Find, to 3 significant figures, the value of h.

Answer 1

13.95 cm

Explanation:

the volume of the cone =

⅓× π r². h = 180 π

⅓×π r²×15 = 180 π

(eliminate π)

=> 5r² = 180

r² = 180/5 = 36

r=√36 = 6 cm

the volume of the sand = ½×4/3 π r³

= ⅔× π ×6³ = 144π cm³

the ratio of the volume :

144π/180π = 0.8

so the value of h = ³√0.8 x 15 = 0.93× 15

= 13.95 cm