Question

rate of 14 per sq. m, if the raulus UI LE vu
OR
A cylindrical container of radius 7 cm and height 30.625 cm is filled with ice-cream. The whole ice-cream has to
be distributed to 15 children in equal cones with hemispherical tops. If the height of the conical portion is tive
times the radius of base, then find the radius of the ice-cream cone.

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Answer 1

Answer given in attachment;

Radius of the ice cream cone is 3.5 cm

Answer 2

Answer:

The radius of each ice-cream cone is 3.9 cm  

Step-by-step explanation:

Given as :

The radius of cylindrical container = r = 7 cm

The height of cylindrical container = h = 30.625 cm

Let Volume of cylindrical container = v  cm³

∵ Volume of cylindrical container = π × radius² × height

Or, v = π × r² × h

Or, v = 3.14 × 7² × 30.625

∴   v = 4711.9625  cm³

Again

The whole ice-cream from cylindrical container is distributed in cone

The height of cone = 5 times the radius of cone

Let The radius of cone = R cm

Let The height of cone = H  cm

Let The volume of cone = V cm³

So, H = 5 R

∵ volume of cone = $\dfrac{1}{3}$ × π × radius² × height

Or, V = $\dfrac{1}{3}$ × π × R² × H

Or, V = $\dfrac{1}{3}$ × π × R² × 5 R

Or, V = $\dfrac{1}{3}$ × 3.14 × 5 R³

Since ice cream is distributed to 15 children in each cone

So, V = 15 ×  $\dfrac{1}{3}$ × 3.14 × 5 R

i.e V = 78.5 R³

Now, Volume of both container and cone equal

i.e Volume of cylinder = volume of cone

Or, V = v

Or, 78.5 R³ = 4711.9625  cm³

Or, R³ = $\dfrac{4711.9625}{78.5}$

Or, R³ = 60.025

i.e R = ∛60.025

∴  R = 3.9 cm

So, The radius of each cone = R = 3.9 cm

Hence, The radius of each cone is 3.9 cm  Answer