Question

একটি লম্ব বৃত্তাকার চোঙের উচ্চতা উহার ব্যাসার্ধের দ্বিগুণ, যদি উচ্চতা 6 গুণ হতাে তবে চোঙাটির আয়তন 539 ঘন
ডেসিমি বেশি হতাে। চোঙটির উচ্চতা কতাে?​

Answer 1

Given:

The vertical height of a round funnel is twice its radius, if the height is 6 times the radius then the volume of the funnel is 539 cubic  decimeter more

To find:

The height of the funnel

Solution:

Let's assume,

"h" → height of the funnel

"r" → radius of the funnel

According to the question, we can solve the problem as follows:

When original height is twice its radius:

i.e., h = 2r

∴ The original volume of the funnel,

V = $\frac{1}{3} \pi r^2 h$

putting h = 2r

$\implies V = \frac{1}{3} \pi r^2 (2r)$

$\implies \bold{V = \frac{2}{3} \pi r^3}$

When height is 6 times its radius:

i.e., h = 6r

∴ New volume of the funnel = [Original volume of the funnel] + 539

$\implies \frac{1}{3} \pi r^2 (6r) = \frac{2}{3} \pi r^3 + 539$

$\implies \frac{6}{3} \pi r^3 = \frac{2}{3} \pi r^3 + 539$

$\implies \frac{6}{3} \pi r^3 - \frac{2}{3} \pi r^3 = 539$

$\implies[ \frac{6 - 2}{3}] \pi r^3 = 539$

$\implies[ \frac{4}{3}] \pi r^3 = 539$

$\implies\frac{4}{3}\times \frac{22}{7} \times r^3 = 539$

$\implies r^3 = \frac{539 \times 3 \times 7}{4 \times 22}$

$\implies r^3 = \frac{11319}{88}$

$\implies r^3 =128.625$

$\implies r = \sqrt[3]{128.625}$

$\implies \bold{r = 5.04}$ ≈ 5 dm

∴ The original height, h = 2r = 2 × 5 = 10 dm

Thus, the height of the funnel is → 10 dm.

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Also View:

An oil funnel of sheet consists of a cylindrical part 10cm long attached to a frustum of a cone. If the total height be 22 cm, diameter of the cylindrical part be 8 cm and the of the top of the funnel be 18 cm, find the area of the sheet required to make funnel.

https://brainly.in/question/256368

A cake decorator rolls a piece of stiff paper to form a cone. She cuts off the tip of the cone and uses it as a funnel to pour decorative sprinkles into small containers. The cone has a radius of 66 cm and a height of 1818 cm.  What is the volume of the cone before the end is cut off?

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Answer 2

வடமொழி நுவாஙஸயடுஏஸயடூஐவகுதூயடஹு நேரம் கழித்து முயற்சிக்கவும் இல்லை இந்த நிலையில்