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Marie has bought a plant which she needs to transfer from its cylindrical pot to the ground. The pot has diameter 10 cm and is 21 cm high. Marie needs to dig a hole 4cm wider and 5cm deeper than the pot. She then inserts the plant and fills in the rest of the hole with extra soil. (i) Calculate the volume of the hole Marie needs to dig. (ii) Before inserting the plant, Marie fills the hole with water. How much water will she need, assuming none of it soaks away? (iii) Marie is planning to paint the outside of the cylindrical pot excluding the top and bottom. Calculate the area to be painted​

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Using known formulas for cylinders, we will get:

  • i) 4,000.36 cm^3
  • ii) 4,000.36 cm^3
  • iii) 1,142.96 cm^2.

Working with cylinders:

We know that the pot has a diameter of 10cm and a height of 21 cm, and the hole must be 4 cm wider (so the diameter is 14cm) and 5 cm deeper (so the height is 26cm).

i) The volume of a cylinder of radius r and height H is given by:

V = pi*r^2*H

Where pi = 3.14, and the radius is half the diameter, so we have:

r = 14cm/2 = 7cm.

Then the volume is:

V = 3.14*(7cm)^2*26cm = 4,000.36 cm^3

ii) To fill a volume of 4,000.36 cm^3, you need 4,000.36 cm^3 of water.

iii) The curve surface of a cylinder is given by:

S = 2*pi*r*H

Remember that:

r = 7cm

H = 26cm.

Replacing that we get:

S = 2*3.14*7cm*26cm = 1,142.96 cm^2

So se must paint an area of 1,142.96 cm^2.

If you want to learn more about cylinders, you can read:

https://brainly.com/question/7194993

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