Answer:
Surface area of larger solid is = 25 square feet.
Step-by-step explanation:
Given that,
Volume of smaller solid = 8 cubic feet
Volume of larger solid = 125 cubic feet
We know that,
Volume is the function of cube of dimensions.
and area is the function of square of dimensions.
So,
8 = 2³
125 = 5³
Ratio of sides = 2 : 5
Ratio of surface area = 4:x (let surface area of larger solid x)
So,
[tex]\frac{4}{x}=\frac{2^{2} }{5^{2} }[/tex]
x = 25 sq ft
surface area of the larger solid = 25 sq ft
That's the final answer.
Answer:
25 square feet
Step-by-step explanation:
We are given that
Volume of smaller solid= 8 cubic feet
Volume of large solid=125 cubic feet
Surface area of smaller solid=4 square feet
We have to find the surface area of larger solid.
Volume of is a cubic function
Ratio of two solids=6:125
[tex]\frac{V_1}{V_2}=\frac{2^3}{5^3}=\frac{a^3}{b^3}[/tex]
[tex]\frac{a}{b}=\frac{2}{5}[/tex]
Where a= Side of small solid
b=Side of large solid
Ratio of corresponding sides of two solids=2:5
When two solids are similar then the ratio of surface area
[tex]\frac{Area\;of\;small\;solids}{area\;of\;larger\;solids}=\frac{a^2}{b^2}[/tex]
Area of small solid: area of larger solid=[tex]\frac{2^2}{5^2}[/tex]
4: area of large solid=4: 25
Area of larger solid=[tex]\frac{4\times 25}{4}=25 ft^2[/tex]
Hence, the area of larger solid=25 square feet
