The required **ratio **of the **length **is 2/3 and the ratio of the **volume **is 8/27.
Given that, Two similar cones have surface areas in the ratio 4:9. To determine the ratio of their lengths and their volumes.
What is the Ratio?
The **ratio **can be defined as the **proportion **of the **fraction **of one **quantity **towards others. e.g.- water in milk.
Here, The surface area of the cone 1 = S₁ The surface area of the cone 2 = S₂ According to the question, r₁/r₂ = h₁/h₂ = l₁/l₂ and, S₁/S₂ = [r₁/r₂]² = 4/9 [r₁/r₂] = 2/ 3 = h₁/h₂ = l₁/l₂ Now, = Volume of cone 1 / volume of cone 2 = [r₁/r₂]²×[h₁/h₂] = 4/9 × 2/3
= 8/27
Thus, the required **ratio **of the **length **is 2/3 and the ratio of the **volume **is 8/27.
Learn more about **ratios **here:
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***Cone : r radius of *** bottom circle, L lateral length, h = perpendicular height
Total surface area = π r² ( 1 + L / r ) Volume = 1/3 π r² h L² = r² + h²
Similar cones => r1 : r2 = L1: L2 = h1 : h2 => L1 / r1 = L2 / r2 ****** => 1+ L1/r1 = 1 + L2/r2***
*** S1 : S2 = 2² : 3² = r1² : r2²***
*** r1 : r2 = 2 : 3 also h1 : h2 = 2 : 3***
*** ***
*** Volumes V1 : V2 = r1² h1 / r2² h2 = (2/3)² 2/3 = 8 / 9***
The ratio of the lengths of the two similar cones is 3 2 and the ratio of their volumes is 27 8 .
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Jawaban:jika Pak Dian menggunakan ¼ kg (250 gram) pupuk untuk 150 pohon per bulan, maka totalnya adalah 37,5 kg atau 37.500 gram per bulan, dan 450 kg atau 450.000 gram per tahun.