Question

Two similar cones have volumes of 4cm³ and 108cm³respectively. If the larger one has surface area 64cm², find the surface area of the smaller one

Answer 1

Given data : Two similar cones have volumes of 4 cm³ and 108 cm³respectively. If the larger one has surface area 64 cm².

To find : The surface area of the smaller one ?

Solution : Here,

For smaller cone :

⟹ volume = V1

⟹ area = A1

⟹ radius = r

⟹ height = h

⟹ slant height = l

For larger cone :

⟹ volume = V2

⟹ area = A2

⟹ radius = R

⟹ height = H

⟹ slant height = L

Now, according to given their are two similar cones hence,

⟹ L/l = H/h = R/r ____( 1 )

Now,

⟹ V2/V1 = {⅓*π*R²*H}/{⅓*π*r²*h}

⟹ 108/4 = {R²*H}/{r²*h}

⟹ 108/4 = {R/r}² * H/h

from {1}

⟹ 108/4 = {R/r}² * R/r

⟹ 108/4 = {R/r}³

⟹ {R/r}³ = 108/4

⟹ R/r = ³√{108/4}

⟹ R/r = ³√27

⟹ R/r = 3

Now,

⟹ A2/A1 = {π*R²*L}/{π*r²*l}

⟹ 64/A1 = {R/r}² * L/l

⟹ 64/A1 = {R/r}² * R/r

⟹ 64/A1 = {R/r}³

⟹ 64/A1 = {3}³

⟹ 64/A1 = 27

⟹ A1 = 64/27

⟹ A1 = 2.37037037 cm²

Answer : Hence, the area smaller cone is 2.37037037 cm²

Answer 2

Step-by-step explanation:

Two similar cones have volumes of 27 cm³ and 1728 cm³ respectively, If the larger one has surface area 800 cm²,, find the surface area of the smaller cone.