Name: Surface Area and Volume of Right Triangular Pyramid
Uploaded: 2019-07-19
Duration: 3 min 52 s
Description: To find the volume of a right triangular pyramid, we use the formula V = (1/3)AH, where A = area of the pyramid's base and H = height of the pyramid. Watch a...

Question

Using a square and four triangles with dimensions as specified in the picture, a pyramid is made.

What is the height of this pyramid?
What if the square and triangles are like this?

Accepted Answer

Let us $a$ be the edge and $l$ be the slant height of the square pyramid.

Square pyramid is made up of above dimensions.
$l = 18, a = 24$

From the above, height is given by
$h = \sqrt{l^{2} - {(\frac{a}{2})}^{2}}$

$\Rightarrow h = \sqrt{{(18)}^{2} - {(\frac{24}{2})}^{2}}$

$\Rightarrow h = \sqrt{18^{2} - 12^{2}}$

$\Rightarrow h = \sqrt{324 - 144} = \sqrt{180}$

$∴ h = 6 \sqrt{5} cm$ .

Hence, height of the pyramid is $6 \sqrt{5} cm$ .

Given,

Now, $l a t e r a l e d g e = 30, a = 24$ .

Slant height is $l = \sqrt{{(l a t e r a l e d g e)}^{2} - {(r a d i u s)}^{2}}$

$l = \sqrt{30^{2} - 12^{2}} = \sqrt{900 - 144} = 6 \sqrt{21}$

$h = \sqrt{l^{2} - {(\frac{a}{2})}^{2}}$

$\Rightarrow h = \sqrt{{(6 \sqrt{21})}^{2} - {(\frac{24}{2})}^{2}}$

$\Rightarrow h = \sqrt{766 - 144}$

$\Rightarrow h = \sqrt{612} = 6 \sqrt{17}$

Hence, height of pyramid is $6 \sqrt{17} cm$ .

Kerala Board Solutions for Chapter: Solids, Exercise 2: Exercise 2

Kerala Board Mathematics Solutions for Exercise - Kerala Board Solutions for Chapter: Solids, Exercise 2: Exercise 2

Questions from Kerala Board Solutions for Chapter: Solids, Exercise 2: Exercise 2 with Hints & Solutions

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