Rivera0685
contestada

The ratio of the volume of two similar solids is 64:729. If the surface area of the larger solid is 567 km2
, find the surface area of the smaller solid.

Respuesta :

asuwafohjames

The surface area of the smaller solid is 112 km².

What are Similar Solids?

Similar shapes are enlargements of two shapes using a scale factor.

The ratio of the volume of similar solids is the ratio of the cube of their length.

Formula:

  • V/v = L³/l³................... Equation 1
  • L/l = ∛(V/v)............... Equation 2

Where:

  • V = Volume of the larger solid
  • v = volume of the smaller solid
  • L = Length of the larger solid
  • l = Length of the smaller solid.

From the question,

Given:

  • V:v = 729/64

Substitute the value into equation 2

  • L/l = ∛(729/64)
  • L/l = 9/4

To calculate the area of the smaller solid, we use the formula below

  • A/a = L²/l²

Where:

  • a = Area of the smaller solid.
  • A = Area of the larger solid

make a the subject of the equation

  • a = (l²A)/L²................ Equation 2

 From the question,

Given:

  • l/L = 4/9
  • A = 567 km²

Substitute these values into equation 2

  • a = (4²/9²)567
  • a = 112 km²

Hence, the surface area of the smaller solid is 112 km².

Learn more about similar shapes here: https://brainly.com/question/2644832

#SPJ1

Otras preguntas