Question

unit 3 study guide
name:
block:
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directions: show work and all formulas used to solve each question. remember you need to show work on the test for full credit

1. here is a rectangle.

which solid results from rotating the rectangle using the axis of rotation shown?
a. rectangular prism
b. cylinder
c. square based prism
d. rectangular based pyramid

1. a container of vegetable oil has a density of 0.70. a manufacturer wants to sell bottles of vegetable oil that contain 147 grams of oil. what is the volume of the container that holds 147 grams of oil?
2. here is a cone. round your answer to the nearest tenth if needed.

a. what is the height of the cone?
b. what is the volume of the cone?

Explanation:

1.

Step1: Comprender la rotación de figuras

Al rotar un rectángulo alrededor de uno de sus lados, se forma un cilindro.

Step1: Recordar la fórmula de densidad

La densidad $
ho=\frac{m}{V}$, donde $
ho$ es la densidad, $m$ es la masa y $V$ es el volumen. Re - arreglamos la fórmula para despejar $V$: $V = \frac{m}{
ho}$.

Step2: Sustituir valores

Dado que $m = 147$ gramos y $
ho=0.70$, entonces $V=\frac{147}{0.70}=210$.

Step1: Aplicar el teorema de Pitágoras en el cono

En un cono, si $l$ es la generatriz, $r$ es el radio y $h$ es la altura, entonces $l^{2}=h^{2}+r^{2}$. Sabemos que $l = 15$ cm y $r = 9$ cm. Re - arreglamos para despejar $h$: $h=\sqrt{l^{2}-r^{2}}$.

Step2: Calcular la altura

$h=\sqrt{15^{2}-9^{2}}=\sqrt{(15 + 9)(15 - 9)}=\sqrt{24\times6}=\sqrt{144}=12$ cm.

Answer:

B. Cilindro

2.