Question

1. In the figure below, ABC ~ PQR.

in given figure, ABC is 4 cm and PQR is 6 cm

If the area of ABC is 40 cm2, what is the area of PQR? Show your work.



2. A science museum has a spherical model of the earth with a diameter of 8.5 m. What is the volume of the model? Use 3.14 for and round your answer to the nearest whole number. Show your work.

(4 points: 1-Work shown, 1-Calculations, 1-Area, 1-Units)

Answer 1

Answer:

1. The area of the triangle PQR is 40 cm^2.

2. 321.4 cubic cm

Step-by-step explanation:

1. We are given two triangles, ABC and PQR, which are similar to each other.

Given that area of the triangle ABC is $40cm^2$, we are to find the area of the triangle PQR.

For that, we can use the ratio method:

$\frac { P Q R } { 4 0 } = \frac { 6 } { 4 }$

Area of triangle PQR = $\frac { 6 \times 40 } { 4 } = 60cm^2$

2. We are given the diameter of a spherical model to be 8.5 cm so its radius will be 4.25 cm.

Finding the volume of the spherical model as we know that the volume of a sphere is given by:

$\frac{4}{3} \pi r^3$

Substituting the given value of radius in the formula to get:

Volume of spherical model = $\frac{4}{3} \times 3.14 \times (4.25)^3$ = 321.4 cubic cm