10 of 25 (19 complete) A square right regular pyramid is formed by cutting, fold

Question

10 of 25 (19 complete) A square right regular pyramid is formed by cutting, folding, and gluing the pattem to the right (a) What is the slant height of the pyramid? (b) What is the lateral surface area of the pyramid? (c) Use the Pythagorean theorem to find the height of the pyramid. d) What is the volume of the pyramid? 318 cm 5 cm 18 cm oem (a) The slant height of the pyramid is cm. (b) The lateral surface area of the pyramid is em2 (c) The height of the pyramid is approximatelycm Round the final answer to two decimal places as needed. Round all intermediate values to two decimal places as needed.) (d) The volume of the pyramid is m Round the final answer to two decimal places as needed. Round all intermediate values to two decimal places as needed.)

Explanation / Answer

Answer to the question is as follows:

a. Slant height = ?

Let this be s

So, applying pythogoaras theorm we have :

(18/2)^2 + s^2 = 15^2

s^2 = 225-81 = 144
s = 12

Slant height =12cm

b. Lateral surface area = a*sqrt(a^2+4h^2) , where a= square base = 18cm
So, LSA = 18*sqrt(18^2 + 4*h^2)

lets calculate height of the pyramid now, so that we can plugin the value of height 'h'

s^2 = h^2 + (18/2)^2
144 = h^2 + 81
h^2 = 63
h = 3sqrt(7)

LSA = 18*sqrt(324+4*63) = 432cm^2

c. Height has been calcualated in part b, as h = 3*sqrt(7)

d. Volume of this square pyramid = a^2 *h/3 = 18^2 *3*sqrt(7)/3 = 857.22 cm^3

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