Question

An inverted cone of vertical height 12 cm and
the radius of base 9 cm contains water to a
depth of 4 cm. Find the area of the interior
surface of the cone not in contact with the
water. ​

Answer 1

Answer:

Only 11.11% of the cone’s interior surface area is in contact with water and the remaining 88.89 % of the cone’s interior surface area is dry.

Step-by-step explanation:

The vertical height (H) of the cone is 12 cm and the radius (R) of the base is 9 cm. So the slant height (L) of the cone = [12^2 + 9^2]^0.5 = [144 + 81]^0.5 =

[225]^0.5 = 15 cm.

Total surface area of the interior of the cone (of the full height of the cone) = 2(pi)RL = 2*(22/7)*9*15 = 848.5714 sq cm.

When the water is filled up to 4 cm depth, we can find the radius of the water surface and the slant height of water in the cone from similar triangles.

For the radius, 12:4::9: (radius of the water surface). Therefore,

radius of the water surface = 4*9/12 = 3 cm.

For the slant height of water in the cone, 12:15::4: (slant height of water in the cone). Therefore,

slant height of water in the cone =15*4/12 = 5 cm.

Total surface area of the interior of the cone in contact with the water = 2(pi)RL = 2*(22/7)*3*5 = 94.2857 sq cm.

Hence the area of the cone not in contact with the water = 848.5714 - 94.2857 = 754.2857 sq cm.

So only 11.11% of the cone’s interior surface area is in contact with water and the remaining 88.89 % of the cone’s interior surface area is dry.

HOPE THIS HELPS

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