Question

applying your skills: volume
learn the figure names and volume formulas as you practice your skills with
word problems.

for the problems below, decide which formula is needed and solve. you may use
your calculator.

1. how many cubic feet of concrete will be

needed for a driveway section that is 10 feet
long, 8 feet wide, and \\( \frac { 1 } { 2 } \\) - foot thick?

1. a cylindrical water tower is half full of water.

how many cubic feet of water are in the tower
if it measures 20 feet high and has a radius of
7 feet?

Explanation:

Problema 1

Step1: Identificar la figura

El problema se refiere a un bloque rectangular (rectangular solid).

Step2: Aplicar la fórmula

La fórmula para el volumen de un rectangular solid es \(V = lwh\), donde \(l = 10\) ft (largo), \(w=8\) ft (ancho) y \(h = \frac{1}{2}\) ft (alto).

$$
LATEXBLOCK0
$$

Step1: Identificar la figura y el volumen total

El problema se refiere a un cilindro. La fórmula para el volumen de un cilindro es \(V=\pi r^{2}h\). Aquí, \(r = 7\) ft (radio) y \(h = 20\) ft (altura).

$$
LATEXBLOCK0
$$

Step2: Calcular el volumen del agua (mitad del volumen total)

$$ V_{agua}=\frac{1}{2}\times V_{total}=\frac{1}{2}\times980\pi = 490\pi $$

Tomando \(\pi\approx3.14\)

$$ V_{agua}\approx490\times3.14=1538.6 $$

Answer:

40 pies cúbicos de concreto.

Problema 2