Question

question 9: standard g.mg
what is the volume of your lamp shade?
a. 125.3 in³
b. 160.3 in³
c. 270.6 in³
d. 1256.64 in³
for questions 10-12 use the following information:
you cut down a tree in your yard and you want to know what volume of wood you have so you can sell it. you measure the diameter of the tree to be about 16 feet. the height of the tree is 100 feet.
question 10: standard g.mg
which shape best models a tree trunk?
a. sphere
b. prism
c. cone
d. cylinder
question 11: standard g.mg
what is the radius of your tree?
a. 8 feet
b. 16 feet
c. 32 feet
d. 4 feet
question 12: standard g.mg
solve for the volume of the tree.
a. 300,000 ft³
b. 30,010 ft³
c. 20,100 ft³
d. 2,000 ft³

Explanation:

Question 9 (Assuming lamp shade is a frustum or other, but maybe a common shape like a frustum of a cone or a cylinder, but since options are given, maybe it's a specific calculation. But without more info, maybe the intended answer is c? Wait, no, let's check Question 10 - 12 first.

Question 10:

A tree trunk is generally cylindrical as it has a circular cross - section (diameter is measured) and a height, with the radius (or diameter) relatively constant along the height, matching a cylinder's shape. A sphere is round in all directions, a prism has polygonal bases, and a cone tapers to a point, which doesn't match a tree trunk.

The radius \( r \) of a circle is half of the diameter \( d \). Given the diameter \( d = 16 \) feet, so \( r=\frac{d}{2}=\frac{16}{2}=8 \) feet.

Step 1: Recall the volume formula for a cylinder

The volume \( V \) of a cylinder is given by the formula \( V=\pi r^{2}h \), where \( r \) is the radius and \( h \) is the height.

Step 2: Identify the values of \( r \) and \( h \)

From Question 11, \( r = 8 \) feet and the height \( h=100 \) feet.

Step 3: Substitute the values into the formula

\( V=\pi\times(8)^{2}\times100=\pi\times64\times100 = 6400\pi\approx6400\times3.1416 = 20096\approx20100\space ft^{3} \)

Answer:

d. Cylinder

Question 11: