Awater tank has the shape of a cone. the tank is 10 m high and has a radius of 3m at the top. of the water is 4 m deep, what is the surface area of the top of the water

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

From the diagram,

/AC/ = 10m, /AB/ = 4m, /CD/ = 3m and /BE/ = r

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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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.

-12 > a

step-by-step explanation:

-11 > 1 + a

subtract 1 from each side

-11-1 > 1-1+a

-12 > a