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

hi,

i'm 75% sure the answer is 1,1 to both lines.

have a great day

the figures below are made out of circles, semicircles, quarter … find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations). remember that we'll also have to cut whatever areas we get in half, since we're only dealing im pretty sure that is the right answer

step-by-step explanation: