Question

the ratio of the volumes of two cubes is 8:27. find the ratio of their surface areas​

Answer 1

$\Large{\underline{\underline{\mathfrak{\bf{Question}}}}}$

the ratio of the volumes of two cubes is 8:27. find the ratio of their surface areas

$\Large{\underline{\underline{\mathfrak{\bf{Solution}}}}}$

$\Large{\underline{\mathfrak{\bf{Given}}}}$

• Ratio of volume of two cubes = 8 : 27

$\Large{\underline{\mathfrak{\bf{Find}}}}$

• Ratio of there surface area

$\Large{\underline{\underline{\mathfrak{\bf{Explanation}}}}}$

Let,

• Volume of first cube = V'
• Volume of second cube = V"
• Side of first cube = S'
• Side of second cube = S"
• Surface area of first cube = S¹
• Surface area of second cube = S²

Formula of volume,

$\boxed{\sf{\underline{\orange{\:Volume_{cube}\:=\:(side)^3}}}}$

By, question condition

$\mapsto\sf{\:volume_{first\:cube}:Volume_{second\:cube}\:=\:8:27} \\ \\ \\ \mapsto\sf{\:V':V"\:=\:8:27} \\ \\ \\ \mapsto\sf{\:(S')^3:(S")^3\:=\:8:27} \\ \\ \\ \mapsto\sf{\:\left(\dfrac{S'}{S"}\right)^3\:=\:\dfrac{8}{27}}$

$\mapsto\sf{\:\dfrac{S'}{S"}\:=\:\left(\dfrac{8}{27}\right)^{\frac{1}{3}}} \\ \\ \\ \mapsto\sf{\:\dfrac{S'}{S"}\:=\:\left(\dfrac{2}{3}\right)^{3\times \frac{1}{3}}} \\ \\ \\ \mapsto\sf{\orange{\:\dfrac{S'}{S"}\:=\:\dfrac{2}{3}}} \\ \\ \\ Or, \\ \\ \\ \mapsto\sf{\red{\:S':S"\:=\:2:3}}$

Now,

$\boxed{\sf{\underline{\orange{\:Surface\:area_{cube}\:=\:6(side)^2}}}}$

Again By, question condition

$\mapsto\sf{\:Surface\:area_{first\:cube}:Surface\:area_{second\:cube}\:=\:6.(S')^2:6.(S")^2} \\ \\ \\ \mapsto\sf{\:\dfrac{S^1}{S^2}\:=\:6\times \dfrac{S'}{S"}} \\ \\ \\ \small\sf{\green{\:\:\:\:keep\:value\:of\:\frac{S'}{S"}\:=\:\frac{2}{3}\:}} \\ \\ \\ \mapsto\sf{\:\dfrac{S^1}{S^2}\:=\:6\times (\dfrac{2}{3})^2} \\ \\ \\ \mapsto\sf{\:\dfrac{S^1}{S^2}\:=\:6\times\dfrac{4}{9}} \\ \\ \\ \mapsto\sf{\:\dfrac{S^1}{S^2}\:=\:\dfrac{8}{3}} \\ \\ \\ Or, \\ \\ \\ \mapsto\sf{\red{\:S^1:S^2\:=\:8:3}}$

$\Large{\underline{\mathfrak{\bf{Hence}}}}$

• Ratio between their surface will be = 8:3

Answer 2

Answer:

volumes of two cubes are in the ratio 8:27 then, the ratio of their surface areas is 4: 9.