What is the slant height of the cone?(1 point)Responses9.8 ft; Use the Pythagorean Theorem9.8 ft; Use the Pythagorean Theorem97 ft; Use the volume formula97 ft; Use the volume formula12 ft; Use the Pythagorean Theorem12 ft; Use the Pythagorean Theorem7 ft; Use the volume formula

triangle 9ft and 8ft

1 answer

To find the slant height of the cone, we can use the Pythagorean Theorem. The slant height \( l \) of the cone is the hypotenuse of a right triangle formed by the radius \( r \), the height \( h \), and the slant height \( l \).

Given:

  • Radius (base of the triangle) = 8 ft
  • Height (perpendicular side of the triangle) = 9 ft

Using the Pythagorean Theorem: \[ l^2 = r^2 + h^2 \] \[ l^2 = 8^2 + 9^2 \] \[ l^2 = 64 + 81 \] \[ l^2 = 145 \] \[ l = \sqrt{145} \approx 12.04 \text{ ft} \]

So the approximate slant height of the cone is 12 ft.

Therefore, the correct response from the options you provided would be: 12 ft; Use the Pythagorean Theorem.