Question

A cylindrical paint bucket is 14 cm high with its capacity of 2816 cm3 approximately how long is the radius of this paint bucket in cm?

Answer 1

Given:-

• Height of the Cylindrical bucket = 14 cm
• Volume of Bucket = 2,816 cm³

To Find:-

• Radius of the Bucket

Formula Used:-

• ${\boxed{\bf{\red{Volume\:of\:Cylinder= \pi r^2h}}}}$

Solution:-

Using Formula,

$\sf :\implies\:Volume\:of\:Cylinder= \pi r^2h$

Putting Values,

$\sf :\implies\:2,816= \dfrac{22}{7}\times r^2 \times 14$

$\sf :\implies\:2,816= 44\times r^2$

$\sf :\implies\:r^2= \dfrac{2,816}{44}$

$\sf :\implies\:r^2= \dfrac{256}{4}$

$\sf :\implies\:r^2= 64$

$\sf :\implies\:r= \sqrt{64}$

$\sf :\implies {\underline{r= 8\:cm}}$

Hence, The Radius of this paint bucket is 8 cm.

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More Formulas for Cylinder:-

• $\bf Total\: Surface\:Area= 2\pi r(h+r)$
• $\bf Curved\: Surface\:Area= 2\pi rh$

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Answer 2

Given :

• Height of Bucket = 14cm
• Capacity of Bucket = 2816cm³

To Find :

• Radius of the Bucket.

Solution :

It is given that the shape of the bucket of is cylindrical and we know volume of cylinder is given by πr²h where r and h stands for radius and height respectively.

Finding the Radius of Bucket :

• Volume = πr²h
• 2816 = 22/7 × r² × 14
• 2816 = 22/7 × 14 × r²
• 2816 = 22 × 2 × r²
• 2816 = 44 × r²
• 2816/44 = r²
• 64 = r
• √64 = r
• 8cm = r

Therefore :

• Radius of the Bucket is 8cm

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