Question

the ratio of the radius of two load barrels bellows is 2:3 and the radio of height is 5:3 find the radio of its volumes
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Answer 1

DIAGRAM:

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\qbezier(-1,0)(0,1)(1,0)\qbezier(-1,0)(0,-1)(1,0)\put(-1,0){\line(0,1){2}}\put(1,0){\line(0,1){2}}\qbezier(-1,2)(0,1)(1,2)\qbezier(-1,2)(0,3)(1,2)\put(1.5,0){\vector(0,1){2}}\put(1.5,0){\vector(0,-1){0.3}}\put(1.7,0.6){ \bf h }\put(0,0){\vector(1,0){1}}\put(1,0){\vector(-1,0){1}}\put(0.3,0.1){ \bf r }\end{picture}$

ANSWER:

• The ratio of their volumes = 20 : 27

GIVEN:

• The ratio of the radius of two load barrels is 2 : 3.

• The ratio of their height is 5 : 3.

TO FIND:

• The ratio of their volumes.

EXPLANATION:

Barrel is in the shape of a cylinder.

$\red{\bigstar{\boxed{\large{\bold{\gray{Volume \ of \ cylinder \ = \pi r^2 h }}}}}}$

$V_1 = \pi {r_1}^2 h_1 | |V_2 = \pi {r_2}^2h_2$

$V_1 = \pi(2)^25 | |V_2 = \pi(3)^2(3)$

$\dfrac{V_1}{V_2}=\dfrac{20\pi}{27\pi}$

$\dfrac{V_1}{V_2}=\dfrac{20}{27}$

HENCE THE RATIO OF THEIR VOLUMES IS 20 :27.

SOME MORE FORMULAE:

$\blue{\bigstar{\boxed{\large{\bold{\gray{C.S.A \ of \ cylinder \ = 2\pi r h }}}}}}$

$\orange{\bigstar{\boxed{\large{\bold{\gray{T.S.A \ of \ cylinder \ = 2\pi r(h+r) }}}}}}$

Answer 2

Answer:

The given question is solved in the uploaded photo.