Respuesta :
Two solids are said to be similar when their corresponding sides and angles are proportional and congruent. Since the solids here are similar, we calculate as follows:
Assuming the solid is a sphere
V1/V2 = r1^3 / r2^3 = 1331/216 = 6.16203
r1/r2 = 11/6
A1/A2 = (r1/r2)^2
324/A2 = (11/6)^2
A2 = 42.84 m^2
Assuming the solid is a sphere
V1/V2 = r1^3 / r2^3 = 1331/216 = 6.16203
r1/r2 = 11/6
A1/A2 = (r1/r2)^2
324/A2 = (11/6)^2
A2 = 42.84 m^2
Answer:
surface area of the smaller solid will be 96.40m².
Step-by-step explanation:
Volumes of two similar solids are 1331 m³ and 216 m³
Since volume is a three dimensional unit means its a multiplication of 3 dimensions, so cube root of ratio of volume gives us the ratio of dimensions.
[tex]\frac{V_{1} }{V_{2}}=\frac{216}{1331}=\sqrt[3]{\frac{216}{1331}}=\frac{6}{11}[/tex]
Similarly ratio of surface areas will be equal to the square of the ratio of dimensions.
[tex]\frac{S_{1} }{S_{2}}=(\frac{6}{11})^{2}[/tex]
[tex]\frac{S_{1} }{324}=(\frac{36}{121})[/tex]
By cross multiplication
[tex]S_{1}(121)=36(324)[/tex]
[tex]S_{1}=\frac{36*324}{121}=96.40m^{2}[/tex]
therefore, surface area of the smaller solid will be 96.40m².
