The water is 4/10 of the full depth, so its surface has a radius that is 4/10 of the radius at the top. Of course, the surface of the water has the shape of a circle.
The area of a circle is given by
... A = π·r²
... A = π·(0.4·3 m)² = 1.44π m²
The surface area of the top of the water is 1.44π m² ≈ 4.524 m².
The surface area of the top of the water is 4.52 m²
An illustrative diagram is shown in the attachment below
To calculate the surface area of the top of the water, we will calculate the area of the circle formed at the top of the water (the red circle in the diagram).
To calculate the area of the circle formed at the top of the water, we will first determine the value of the radius, r.
Consider the triangle (brought out from the cone) beside the cone.
ΔACD and ΔABE are similar triangles
Then, by similarity, we can say that
[tex]\frac{/AC/}{/AB/}=\frac{/CD/}{/BE/}[/tex]
From the diagram,
/AC/ = 10m, /AB/ = 4m, /CD/ = 3m and /BE/ = r
[tex]\frac{10}{4}=\frac{3}{r}[/tex]
10r = 3×4
10r = 12
r = 12/10
∴ r = 1.2 m
Area of a circle is given by the formula
A = πr²
Where A is the area and r is the radius
Then, for the area of the circle formed at the top of the water,
A = π × 1.2²
(Take π = 3.14159)
A = 3.14159 × 1.2²
A= 3.14159 × 1.44
A = 4.52 m²
Hence, the surface area of the top of the water is 4.52 m²
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