Question

the perimeters of the ends of frustum of a cone are 44cm and 22 cm if the height of the frustum be 21 cm. find its radii slat height and volume ​

Answer 1

Step-by-step explanation:

the perimetcone are 44cm and 22 cm if the height of the frustum be 21 cm. find its radii slat height and volume21 cm. find its radii slat heighters of the ends of frustum of a cone are 44cm and 22 cm if the height of the frustum be the perimeters of the ends of frustum of a and volume

Answer 2

The radii are 7 cm and 3.5 cm

slant height is 20.7 cm

volume of frustum is 1886.5 cm ³

Step-by-step explanation:

perimeter of one end = 44 cm

$2\pi r_1 = 44\\\\r_1 =\frac{22\times 7}{22}\\\\r_1=7 cm$

similarly perimeter of other end = 22 cm

$2\pi r_2 = 22\\\\r_2 =\frac{11\times 7}{22}\\\\r_2=\frac{7}{2} cm= 3.5 cm$

height of the frustum = 21 cm

slant height

$l= \sqrt{h^2-(r_1-r_2)^2}\\\\l= \sqrt{21^2-(7-3.5)^2}\\\\l= \sqrt{441-(3.5)^2}\\\\ l= \sqrt{441-12.25}\\\\l=\sqrt{428.75 cm} = 20.7 cm$

volume of frustum

$\frac{1}{3}\pi h (r_1^2+r_2^2+r_1r_2)\\\\\frac{1}{3}\times \frac{22}{7}\times 21\times (7^2+3.5^2+7\times 3.5)\\\\\frac{1}{3}\times \frac{22}{7}\times 21\times(85.75)\\\\=1886.5 cm^3$

hence , The radii are 7 cm and 3.5 cm

slant height is 20.7 cm

volume of frustum is 1886.5 cm ³

#Learn more:

The perimeter of the ends of the frustum of a cone are 36 cm and 48cm. if the height of the frustum is 11 cm find its volume

https://brainly.in/question/8542017