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Mathematics

Grade-8

Easy

Question

A paper party hat, like the one shown, has a height of 8 inches and a radius of 4 inches. How many square feet of cardboard would be needed to create this hat?

112.40 in.²
10 in.²
50 in.²
22.5 in.²

hint Hint:

The area needed will be equal to the lateral surface area of the cone. The total surface area of the cone is $pi r l$ , where r is the radius of the cone and l is the slant height of the cone.

The correct answer is: 112.40 in.²

The total surface area of the cone is $pi r l$ , where r is the radius of the cone and l is the slant height of the cone.
In this question we are given the height and radius of the cone and we have to calculate the slant height of the cone for calculating the total surface area.
Step1: Calculating the slant height of the cone.
we know that the slant of the cone is given by
$l equals square root of r squared plus h squared end root$
=> $l equals square root of 4 squared plus 8 squared end root$
=> $l equals 8.94$
Step2: Now we will calculate the Total surface area by putting the values of r and l in the formula of total surface area
Total Surface Area = $pi r l$
=> $pi cross times 4 cross times 8.94$
=> $112.40 space i n squared$

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