A flower vase is in the form of a frustum of a cone. the perimeter of it's bases are 44cm^2 and 8.4πcm^2.if the depth is 14 cm.find the volume of the vase.
I have got the answer that is apxm.74.9cm^3
is the answer right?
Answers
Step-by-step explanation:
top of perimeter of frustum = 2πr1
r1 = 44 × 7/ 2 × 22
= 7cm
base perimeter r2 = 8.4π
8.4π = 2πr
π cancels hope u understand
r2 = 8.4/2
= 4.2
h = 14cm
r1 = 7cm
r2 = 4.2cm
volume of frustum
= 1/3 πh ( r1^2 + r2^2 + r1 × r2 )
= 1/3 × 22/7 × 14 ( 7^2 + 4.2^2 + 7×4.2 )
= 44/3 ( 49 + 17.64 + 29.4 )
= 44/3 × 96
= 44 × 32
= 1408cm^3
Step-by-step explanation:
:
Step 1:
Let the perimeter and radius of the bases be “P₁” & “R₁” and “P₂” & “R₂” respectively.
It is given that,
Perimeter, P₁ = 2πR₁ = 44 cm
∴ R₁ = 44/2π = 22 * 7/22 = 7 cm
And,
Perimeter, P₂ = 2πR₂ = 8.4π cm
∴ R₂ = 8.4π / 2π = 4.2 cm
Step 2:
The depth of the frustum cone, h = 14 cm
We know,
The volume of the flower vase which is in the form of frustum cone is,
= * π * [R₁² + R₂² + (R₁ * R₂)] * h
= * [(7)² + (4.2)² + (7 * 4.2)] * 14
= * [49 + 17.64 + 29.4] * 14
= 2 * * 96.04
= 1408.58 cm³
Thus, the flower vase can hold 1408.58 cm³ of soil.
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