What is the slant height of the given pyramid to the nearest whole unit?
a. 7 cm
b. 11 cm ***
c. 13 cm
d. 16 cm
To find the slant height of a pyramid, we need to use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle formed by the height of the pyramid and half the base of the pyramid.
In this case, we are not given the height of the pyramid or the length of the base. Without this information, we cannot determine the slant height. Therefore, the correct answer is none of the options provided.
To find the slant height of a pyramid, we need to use the Pythagorean Theorem. The slant height is the hypotenuse of a right triangle formed by the height of the pyramid (a vertical line from the apex to the base) and half the length of the base.
Since we don't have the height and the base length given in the question, we need to make an assumption to proceed. Let's assume the height is 10 cm and the base length is 8 cm.
Using the Pythagorean Theorem, we can calculate the slant height:
slant height^2 = height^2 + (base length/2)^2
slant height^2 = 10^2 + (8/2)^2
slant height^2 = 100 + (4)^2
slant height^2 = 100 + 16
slant height^2 = 116
To find the approximate value of the slant height, we take the square root of 116:
slant height ≈ √116
slant height ≈ 10.77
From the given options, the nearest whole unit to 10.77 cm is 11 cm. Therefore, the correct answer is b. 11 cm.