Question

1 which part of a sphere is the longest straight line that can be drawn through it?
a. diameter
b. radius
c. circumference
d. surface area

2 in a right pyramid, what angle does the height make with the base?
a. 30 degrees
b. 60 degrees
c. 90 degrees
d. 45 degrees

3 which of the following is an example of a cone used in a practical scenario?
a. cube
b. sphere
c. traffic cone
d. cylinder

4 which part of a cone is perpendicular to the base?
a. height
b. diameter
c. radius
d. slant height

5 what is the distance from the center of a sphere to any point on the surface called?
a. volume
b. radius
c. circumference
d. diameter

6 what mathematical constant is used in the formula for the volume of a sphere?
a. avogadros number
b. eulers number
c. pi
d. the golden ratio

7 the volume of a pyramid is 150 cubic meters and the height is 10 meters. if the base is a square, what is the side length of the base?
a. 4.7 m
b. 5 m
c. 5.5 m
d. 7 m

Explanation:

Step1: Solve Q1 (Sphere's longest line)

The longest straight line through a sphere passes through its center, connecting two opposite surface points. This is defined as the diameter.

Step2: Solve Q2 (Right pyramid angle)

By definition, the height of a right pyramid is perpendicular to its base, forming a 90-degree angle.

Step3: Solve Q3 (Practical pyramid example)

A traffic cone has a circular base and a pointed apex, matching the shape of a right circular pyramid.

Step4: Solve Q4 (Cone's perpendicular part)

The height of a cone is the segment that runs vertically from the apex to the center of the base, forming a right angle with the base.

Step5: Solve Q5 (Sphere center to surface distance)

The distance from the center of a sphere to any point on its surface is defined as the radius.

Step6: Solve Q6 (Sphere volume constant)

The formula for the volume of a sphere is $V=\frac{4}{3}\pi r^3$, which uses the mathematical constant $\pi$ (pi).

Step7: Solve Q7 (Pyramid base side length)

The volume of a pyramid is $V=\frac{1}{3}Bh$, where $B$ is the area of the square base. Rearrange to solve for $B$:
$B = \frac{3V}{h} = \frac{3\times150}{10} = 45$
Since $B$ is the area of a square, the side length $s = \sqrt{B} = \sqrt{45} \approx 6.7$ m.

Answer:

1. a. Diameter
2. c. 90 degrees
3. c. Traffic cone
4. a. Height
5. b. Radius
6. c. $\pi$
7. a. 6.7 m