Question

A toy is in the shape of the cone over a hemisphere of radius 8 cm.if the total height of the toy is 14 cm, then what is the total surface area of the toy?

Answer 1

hey buddy ,

as , total height of toy = 14 cm
we know that , radius of a hemisphere is its height , so , height of hemisphere = 8 cm

height of cone = total height - height of hemisphere

since , open portion of hemisphere will be the base of cone ,
hence , radius of cone = radius of hemisphere = 8cm
=> height of cone = 14-8 = 6 cm

slant height of cone = √(r²+h²) = √(64+36)= √ 100 = 10 cm.

total surface area of toy = CSA of cone + CSA of hemisphere

=> TSA of toy = πrl + 2πr²

=> TSA of toy = (22/7 × 8 × 10) + (2×22/7×8×8)


=> TSA of toy = {22/7×8×10} + {2×22/7×8×8}

=> TSA of toy = (1760/7)+(44×64/7)

=> TSA of Toy = 251.4 cm² + (402.2) cm²



=> TSA of toy= 653.6 cm² (approx)

hope this helps

Answer 2

Hello dear,
radius of hemisphere = 8cm

height of hemisphere =8cm

radius of cone =8cm

height of cone =14cm-8cm=6cm

slant height = l
=>
$\sqrt{( {8 }^{2} + {6}^{2} )} = \sqrt{100} = 10$

T.S.A. of the toy =C.S.A. of cone+C.S.A. of hemisphere

πrl+2πr2 

  =>πr(l+2r)
$\frac{22}{7} \times 8(10 + 2 \times 8) \\ = > \frac{22}{7} \times 8 \times 26 \\ = > \frac{4576}{7} c {m}^{2} = 652.42c {m}^{2}$
hence TSA of the toy is 652.42cm2