A solid is made by mounting a cone into a hemisphere.the total surface area of the solid is 361.1cm2.if the slant height of the cone is 13cn find the total height of the solid.
Answers
Answer:
17 cm
Step-by-step explanation:
Surface area of the solid = lateral surface area of the cone + lateral surface area of the hemisphere.
= πrs+ 2πr^2
r – Radius of hemisphere or radius of cone bottom. (Both are same as cone is mounted on hemisphere.)
s = Slant height of cone = 13cm.
Surface area of solid = πrs+2πr^2 = π(2r^2+13r)=361.1=3611/10
2r^2+13r=3611*7/(22*10)=25277/220
440r^2+2860r-25277=0
Solving the quadratic equation
(r – 4.996) (r + 11.496) = 0
Radius r = 4.996 ~ 5.0 (Radius cannot be -11.496)
Height of the cone forms a right angle traingle with radius and slant height.
Height of cone^2 = Slant height ^ 2. - radius^2
Height of cone ^ 2 = 13 * 13 – 5*5 = 169 – 25 = 144
Height of cone = √144 = 12cm.
Total height of the solid = height of the cone + radius = 12 + 5 = 17cm.
*answer*
For all figures,
r=7 cm
l (slant height)= h (height of cylinder)=4 cm
T.S.A of the figure= C.S.A of Cone+C.S.A of cylinder +C.S.A of hemisphere.
CSA of cone: πrl=(3.14)×(7cm)×(4cm)=87.92 cm
2
CSA of cylinder: 2πrh=(2)×(3.14)×(7cm)×(4cm)=175.84 cm
2
CSA of hemisphere: 2πr
2
=(2)×(3.14)×(7cm)
2
=307.72 cm
2
Adding all: TSA of figure= 571.48 cm
2
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