The base of a pyramid is a rectangle 40 m long and 20 m wide. The slant height of the pyramid from the mid-point of the shorter side of the base to the apex is 29 m. What is the volume of pyramid?

$5600 m^{3}$

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$400 m^{3}$

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$6500 m^{3}$

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$1753 \sqrt{110} m^{3}$

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Solution

The correct option is A
$5600 m^{3}$

Base area = area of rectangle = 40 $\times$ 20 = 800
$h e i g h t^{2} = (s l a n t h e i g h t)^{2} - (20)^{2}$
= $(29)^{2} - (20)^{2} = 441$
height = 21 m
Area of pyramid = $\frac{1}{3} \times b a s e a r e a \times h e i g h t = \frac{1}{3} \times 800 \times 21$ = 5600 $m^{3}$

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The base of a pyramid is a rectangle 40 m long and 20 m wide. The slant height of the pyramid from the mid-point of the shorter side of the base to the apex is 29 m. What is the volume of pyramid?

The correct option is A 5600 m3 Base area = area of rectangle = 40×20 = 800 height2=(slant height)2−(20)2 =(29)2−(20)2=441 height = 21 m Area of pyramid = 13×base area×height=13×800×21 = 5600 m3