¿Todavía tienes preguntas de matemáticas?

Pregunte a nuestros tutores expertos
Algebra
Pregunta

11. Andrew and Sarah were asked to solve the follo...

11. Andrew and Sarah were asked to solve the following problem: A prism has a base area \( 20 cm ^ { 2 } \) and a height of \( 8 cm \) . The figure is dilated by a scale factor of \( 1 / 4 \) . What is the volume of the new image? Andrew said the volume of the new image is \( 10 cm ^ { 3 } \) because \( 1 / 4 \) of \( 20 \) is \( 5 \) and \( 1 / 4 \) of \( 8 \) is \( 2 \) . So, using the formula base \( \times \) height, you get \( 5 \times 2 = 10 \) . Sarah said the volume of the new image is \( 2.5 cm ^ { 3 } \) because the original volume was \( 20 * 8 = 160 cm ^ { 3 } \) , and \( \frac { 1 } { 4 } * \) 

\( \frac { 1 } { 4 } * \frac { 1 } { 4 } = \frac { 1 } { 64 } \) , so the new volume is \( 160 * \frac { 1 } { 64 } = 2.5 \) . 

Who is correct, and what was wrong with the other person's method? 

Answer

Sarah is correct because it takes into account all 3 dimensions of the prism, that is length, breadth, and height.

Solución
View full explanation on CameraMath App.