question
2. a vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. the diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. find the inner surface area of the vessel.
480
given: volume of cylinder = 1617 cm3let r be the radius of base and h be the height of coner:h = 2:3∴ r/h = 2/33r = 2hh = 3r/2 …(i)formula: volume of cylinder = πr2h∴ 1617 = (22/7) r2hr2h = 514.5using (i) we have∴ r2 × (3r/2) = 514.53r3 = 1029r3 = 343r = 7 cmh = 21/2 cmtotal surface area of cylinder = 2πr2 + 2πrh= 2 × (22/7) × 72 + 2 × (22/7) × 7 × (21/2)= 308 + 462= 770 cm2therefore total surface area of cylinder = 770 cm2 radius = 1.75 m
height (h) = 12 m
volume = 
= ×  × 1.75 × 1.75 × 12
= 38.5 m3
since, 1 m3 = 1 kiloliter
capacity of the pit = (38.5 × 1)
= 38.5 kilolitres area of a semi-circle= 77 m2 vertical and horizontal given:volume of given cube = 64cm3side = a cmvolume = (a)364 = (a)3a = 4cmtwo cubes are joined together.length of resultant cube = 4+4 = 8cmbreadth = 4cmheight = 4cm(a) lsa of cuboid = 2(lh+hb)= 2(8(4) + 4(4))= 2(32+16)= 2(48) = 96cm2⇒ lsa of cuboid = 66m2(b)tsa of cuboid = 2(lh+hb+lb)= 2(8(4) + 4(4) + 8(4))= 2(32+16+32)⇒ tsa of cuboid = 2(80) = 160m2 the north pole sits on a floating ice sheet which is called the arctic ice sheet. there is no land underneath it, but the sea depth at the north pole has been measured at 4,261 metres (13,980 ft). because of this, the north pole is incapable of supporting any plant or animal life on it. sin(α β) = sinαcosβ cosαsinβ 
sin(α-β) = sinαcosβ - cosαsinβ


cos(α β) = cosαcosβ - sinαsinβ
cos(α-β) = cosαcosβ sinαsinβ


tan(α β) = tanα tanβ / 1-tanα tanβ
tan(α-β) = tanα-tanβ / 1 tanα tanβ


sin2θ = 2sinθcosθ = 2tanθ /1 tanθtanθ


cos2θ = cos平方θ−sin平方θ = 2cos平方θ−1 = 1−2sin平方θ


△abc=海龍公式 √s(s-a)(s-b)(s-c) 
[s=a b c/2 ，就是周長/2 ]



△abc=1/2 ａ.b*sinc = axbxc / 4r = rxs 

 [r=外接圓半徑，r=內接圓半徑]




應該是這樣吧!希望對你有幫助。 dear sandra the bottom cake should be a round cake and top should be a hemisphere ..then carve the down portion into a hemisphere to suit the top…then the cake wud be sturdy even with whipping cream and does not move…of course you have dowel them hope this helps given;y-axis, y = cos x and y = sin x, 0 ≤ x ≤ π/2⇒ sin x = cos xrequired area= (√2 − 1) sq.units you don't say that the area must be a rectangle. the true largest area would be a circle, with the circumference equal to 400m and the area would be 12,732.4 m^2. however, evidently, the area is restricted to a rectangle, in which case the maximum area is a square, and the side of the square will be 
400/4 = 100 m. the area is 100x100 = 10,000 m^2.
algebraically,
let x = one pair of opposite sides
(400-2x)/2 = 200-x = the other pair of opposite sides

area = a(x) = x(200 - x) = -x^2 + 200x
x-coordinate of vertex = -b/2a = 200/2 = 100
a(100) = 10,000

that's it! ;)