Question

1)Forty solid hemisphere each of diameter 2cm , are melted to form a solid cone with a base diameter 6cm .Find the height of the cone?

2)A pyramid has a square base of side 12cm and a height of 15cm .Calculate its volume and total surface area?

Answer 1

V = 40 (4/3) pi r^3
r = 1
V = (160/3) pi

V = (1/3)pi r^2 h

(160/3) pi = (1/3) pi 3^2 h
160 = 9 h
h = 160/9

2)
(1/3) 144 (15) = V

distance up slope of side :
15^2 + 6^2 = L^2
L = sqrt (225+36) = sqrt(261)
area of one side = (1/2)(12)sqrt 261
area of 4 sides = 24 sqrt 261
It is not clear if we should add the bottom area
If so then 144+24 sqrt 261

Answer 2

1) 8.88