Geometry 3D - GED Math

1. What is the volume formula for a sphere?

   $V = \frac{4}{3}\pi r^3$, where $r$ is the radius.

2. What is the volume of a cube with edges of $4$ cm?

   $64$ cubic cm. $V = s^3 = 4 \times 4 \times 4$.

3. What is the volume formula for a rectangular prism?

   $V = lwh$ (length times width times height), which is the base area times the height.

4. What is the volume formula for a cylinder?

   $V = \pi r^2 h$: the area of the circular base times the height.

5. What is the surface area of a box that is $2$ by $3$ by $4$ units?

   $52$ square units. $SA = 2(lw + lh + wh) = 2(6 + 8 + 12)$.

6. In the cone surface area formula $SA = \pi rs + \pi r^2$, what does $s$ stand for?

   The slant height: the distance from the tip down the side to the edge of the base, not the vertical height.

7. What is the surface area of a cube with edges of $3$ in?

   $54$ square in. A cube has $6$ square faces, each $3^2 = 9$.

8. How does the volume of a cone compare with a cylinder of the same base and height?

   It is one third as large: $V = \frac{1}{3}\pi r^2 h$. A pyramid is likewise one third of the matching prism.

9. When does a problem call for volume rather than surface area?

   When it asks how much fits inside (filling, holding) in cubic units. Surface area covers the outside (painting, wrapping) in square units.

10. In the formula $V = Bh$ for a prism or cylinder, what does $B$ stand for?

    The area of the base, not the length of a base edge.

11. What is the volume of a cylinder with radius $2$ and height $5$?

    $20\pi$. $V = \pi r^2 h = \pi(4)(5)$.

12. A pyramid has a base area of $30$ square ft and a height of $6$ ft. What is its volume?

    $60$ cubic ft. $V = \frac{1}{3}Bh = \frac{1}{3}(30)(6)$.

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