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.

13.95 cm

Step-by-step 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

the answer is 0.3175 hope that you ^w^

also you might actually want to put this picture up if you want people to solve it luckily i remember this question

trapezoid

step-by-step explanation:

first i plotted all my points on a grid graph

i made sure all of them were in the correct quadrant

then i saw it was a trapezoid or a quadrilateral