the radius and height of a cylinder are in the ratio 3:4 and it's volu

1.	the radius and height of a cylinder are in the ratio 3:4 and it's volume is 38808cm find it's radius and height
Answer» GIVEN :- the radius and height of a CYLINDER are in the ratio 3:4 . Volume of cylinder = 38808 cm³. TO FIND :- The Radius and Height of the cylinder. SOLUTION :- Let the ratio CONSTANT be "x". ★ Radius = 3x. ★ Height = 4x. $\\ : \implies \displaystyle \sf \:volume \: of \: cylinder = \pi r ^{2} h \\ \\$ h = Height of the cylinder. r = Radius of the cylinder. $\\ \\ : \implies \displaystyle \sf \:38808 = \frac{22}{7} \times (3x) ^{2} \times 4x \\ \\ \\$ $: \implies \displaystyle \sf \:38808 = \frac{22}{7} \times 9x ^{2} \times 4x \\ \\ \\$ $: \implies \displaystyle \sf \:38808 = \frac{22}{7} \times 36x ^{3} \\ \\ \\$ $: \implies \displaystyle \sf \:36x ^{3} = \frac{38808 \times 7}{22} \\ \\ \\$ $: \implies \displaystyle \sf \:36x ^{3} = 1764 \times 7 \\ \\ \\$ $: \implies \displaystyle \sf \:36x ^{3} = 12348 \\ \\ \\$ $: \implies \displaystyle \sf \: x ^{3} = \frac{12348}{36} \\ \\ \\$ $: \implies \displaystyle \sf \: x ^{3} = 343 \\ \\ \\$ $: \implies \displaystyle \sf \: x = \sqrt[3]{343} \\ \\ \\$ $: \implies \displaystyle \sf \: x = \sqrt[3]{7 ^{3} } \\ \\ \\$ $: \implies \underline{ \boxed{\displaystyle \sf \: x = 7}} \\ \\$ Now by substituting the value of x we will FIND the radius and the height of the cylinder. ★ Radius = 3x = 3 × 7 = 21 cm ★ Height = 4x = 7 × 4 = 28 cm.

the radius and height of a cylinder are in the ratio 3:4 and it's volume is 38808cm find it's radius and height

Answer»

GIVEN :-

TO FIND :-

SOLUTION :-

Let the ratio CONSTANT be "x".

★ Radius = 3x.

★ Height = 4x.

$\\ : \implies \displaystyle \sf \:volume \: of \: cylinder = \pi r ^{2} h \\ \\$

$\\ \\ : \implies \displaystyle \sf \:38808 = \frac{22}{7} \times (3x) ^{2} \times 4x \\ \\ \\$

$: \implies \displaystyle \sf \:38808 = \frac{22}{7} \times 9x ^{2} \times 4x \\ \\ \\$

$: \implies \displaystyle \sf \:38808 = \frac{22}{7} \times 36x ^{3} \\ \\ \\$

$: \implies \displaystyle \sf \:36x ^{3} = \frac{38808 \times 7}{22} \\ \\ \\$

$: \implies \displaystyle \sf \:36x ^{3} = 1764 \times 7 \\ \\ \\$

$: \implies \displaystyle \sf \:36x ^{3} = 12348 \\ \\ \\$

$: \implies \displaystyle \sf \: x ^{3} = \frac{12348}{36} \\ \\ \\$

$: \implies \displaystyle \sf \: x ^{3} = 343 \\ \\ \\$

$: \implies \displaystyle \sf \: x = \sqrt[3]{343} \\ \\ \\$

$: \implies \displaystyle \sf \: x = \sqrt[3]{7 ^{3} } \\ \\ \\$

$: \implies \underline{ \boxed{\displaystyle \sf \: x = 7}} \\ \\$

Now by substituting the value of x we will FIND the radius and the height of the cylinder.