Answers

The Brainliest Answer!
2014-12-02T17:30:37+05:30

This Is a Certified Answer

×
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Since the cones are similar so l₁/l₂ = r₁/r₂
the the volumes are v₁ 12π unit³ , v₂ = 96π unit³ 
so curved surface area = 15π unit²

so v₂/v₁ =  96π/12π 
     (πr₁²l₁)/(πr₂²l₂) = 8             cancelling 3

⇒ (r₂²l₂)/(r₁²l₁) = 8         

⇒ (\frac{r^2_2}{r^2_1})^2*\frac{l_2}{l_1}=8

⇒ r₂³/r₁³ = 8   using l₁/l₂ = r₁/r₂

⇒ r₂/r₁ = 2

so curved surface area of the unknown cone be x

so cs₂/cs₁ = x/15π

⇒ πr₂l₂/πr₁l₁ = x/15π

⇒ r₂/r₁ x l₂/l₁ = x/15π

⇒ r₂²/r₁² = x/15π               using r₂³/r₁³ = 8

⇒ 4 = x/15π

⇒ x = 60π ANSWER

11 3 11
good effort thanx.............................
thank u so much
welcome and plz mark as best
any question plz ask
thank you
2014-12-03T05:58:22+05:30

This Is a Certified Answer

×
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Let  R = radius of base and L = lateral height,  H = height of cone.

curved surface or lateral surface = A =  π R L ,  and    volume = V = π/3* R² H,

Similar cones have the same (cone) angle at the apex.  Hence the same ratios among R,  H and L.   Let Cone 1 be the larger cone.

       Let  R₂ = x R₁,  H₂ = x H₁  and  L₁ = x L₂

       V₁ / V₂ = π R₁² H₁ / π R₂² H₂  = x³ = 96 π / 12 π  = 8

                   Hence  x = 2 

     Lateral Surface areas A₁ / A₂ = π R₁ L₁ / π R₂ L₂   =  x²  = 4 ,    as x = 2

     A₁ = 4 A₂ = 4  * 15 π = 60 π square units.

6 4 6