# A cone has a height of #12 cm# and its base has a radius of #6 cm#. If the cone is horizontally cut into two segments #6 cm# from the base, what would the surface area of the bottom segment be?

Total surface area of bottom segment is

By signing up, you agree to our Terms of Service and Privacy Policy

To find the surface area of the bottom segment of the cone, we need to calculate the curved surface area of the cone and subtract the area of the smaller cone created by the horizontal cut.

The formula for the curved surface area of a cone is: π × radius × slant height.

First, we need to find the slant height (l) of the original cone using the Pythagorean theorem: l = √(h^2 + r^2), where h is the height and r is the radius of the cone.

Substituting the given values: l = √(12^2 + 6^2) l = √(144 + 36) l = √180 l ≈ 13.42 cm (rounded to two decimal places).

Now, we can find the curved surface area (CSA) of the original cone: CSA = π × r × l CSA = π × 6 × 13.42 CSA ≈ 253.55 cm² (rounded to two decimal places).

Next, we calculate the radius (r') and slant height (l') of the smaller cone created by the horizontal cut: r' = r = 6 cm (radius remains the same) h' = h - 6 = 12 - 6 = 6 cm (height is reduced by 6 cm) l' = √(h'^2 + r'^2) l' = √(6^2 + 6^2) l' = √(36 + 36) l' = √72 l' ≈ 8.49 cm (rounded to two decimal places).

Now, we can find the curved surface area (CSA') of the smaller cone: CSA' = π × r' × l' CSA' = π × 6 × 8.49 CSA' ≈ 160.92 cm² (rounded to two decimal places).

Finally, to find the surface area of the bottom segment, we subtract CSA' from CSA: Surface area of bottom segment = CSA - CSA' Surface area of bottom segment ≈ 253.55 cm² - 160.92 cm² Surface area of bottom segment ≈ 92.63 cm² (rounded to two decimal places).

Therefore, the surface area of the bottom segment of the cone is approximately 92.63 square centimeters.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #60 # and the height of the cylinder is #15 #. If the volume of the solid is #7 pi#, what is the area of the base of the cylinder?
- A chord with a length of #4 # runs from #pi/12 # to #pi/3 # radians on a circle. What is the area of the circle?
- Cups A and B are cone shaped and have heights of #35 cm# and #21 cm# and openings with radii of #7 cm# and #11 cm#, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?
- A box has dimensions of 17 inches long, 1.3 feet wide, and 8 inches high. What is the volume of the box?
- A square has sides of length #s#. A rectangle is #6# inches shorter than the square and #1# inch longer. How do you write an expression to represent the perimeter of the rectangle?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7