Question

base of a pyramid in a square side of the square is 8cm height is 10cm slant height is 12cm find LSA ,TSA and volume​

Answer 1

Given

• Side Of The Pyramid= 8cm.
• Height= 10cm
• Slant Height Is 12cm

To Find

• LSA ,TSA and volume

Formula Used

• $\sf{\gray{LSA \: Of \: Square \: Pyramid = \dfrac{1}{2} Perimeter× Slant \: Height}}$
• $\sf{\gray{TSA \: Of \: Square \: Pyramid = \dfrac{1}{2} Perimeter× Slant \: Height+Base}}$
• $\gray{ \sf \: Volume= \dfrac{1}{3}Side²×Height}$

Solution

• Side Of The Pyramid= 8cm.
• Perimeter of Pyramid=8×4=32cm
• Base area= Side²=8²=64cm²
• Height= 10cm
• Slant Height Is 12cm

LSA of pyramid

$\sf{LSA \: Of \: Square \: Pyramid = \dfrac{1}{2} Perimeter× Slant \: Height}$

Putting the value of perimeter and Height in Formula We get,

$\sf{\implies LSA \: Of \: Square \: Pyramid = \dfrac{1}{2} \times 32× 12}$

$\sf{\implies LSA \: Of \: Square \: Pyramid = 32× 6}$

$\sf{\implies LSA \: Of \: Square \: Pyramid = 192 {cm}^{2} }$

Now TSA of Pyramid

$\sf{TSA \: Of \: Square \: Pyramid = \dfrac{1}{2} Perimeter× Slant \: Height+Base}$

Putting the value of perimeter , Height and Base in Formula We get,

$\sf{\implies TSA \: Of \: Square \: Pyramid = \dfrac{1}{2} \times 32× 12+64}$

$\sf{\implies TSA \: Of \: Square \: Pyramid = ( 32×6)+64}$

$\sf{\implies TSA \: Of \: Square \: Pyramid = 192+64}$

$\sf{\implies TSA \: Of \: Square \: Pyramid = 256 {cm}^{2} }$

Volume Of Pyramid

$\sf \: Volume= \dfrac{1}{3}Side²×Height$

Putting the value of Side and Height in Formula

$\implies\sf \: Volume= \dfrac{1}{3} \times 8²×10$

$\implies\sf \: Volume= \dfrac{1}{3} \times 64×10$

$\implies\sf \: Volume= 21.3×10$

$\implies\sf \: Volume= 213 {cm}^{3}$

• LSA of pyramid= 192cm²
• TSA of Pyramid=256cm²
• Volume Of Cylinder=213cm²