How many cone-shaped party caps of slant height 16cm and diameter 14cm can be made from a cardboard measuring 3168 square cm?
Answers
Answer:
9
Step-by-step explanation:
Lateral area of cone = πr√h^2+r^2
Diameter 14cm = radius 7cm
Slant height 16cm
Use pythag (for right triangle sides) where bottom leg is 7cm and hypotenuse is 16cm, the last leg is about 14.387cm.
Put that into the formula and the lateral area is 351.85cm
ALTERNATE: Lateral area = 1/2pl (perimeter, slant height)
Circumfrence = 2πr, r=7, circumfrence = 43.982cm (which is now the perimeter)
You are given slant height (16).
1/2 * 43.982 * 16 = 351.856cm
You can round both ways to 351.9cm.
3168/351.9=9.0025, so you can make 9 caps in total.
Number of caps that can be formed = 9
Given:
The measure of the cardboard = 3168 cm²
The slant height of the cone is 16cm and the diameter is 14cm
To find:
How many cone-shaped party caps can be formed
Solution:
Formula used:
Curved surface area of the cone = πrl
Where l = Slant height and r = radius of the cone
No of caps can be formed = [ Area of cardboard ]/[Area of cap ]
From the data,
Slant height l = 16 cm
Diameter d = 14 cm
Radius of the cone = 14/2 = 7 cm
From the formula,
Curved surface area of cone cap = π(7)(16)
= (22/7) (7) (16) = 352 cm²
Number of caps formed = [3168 cm² ]/[ 352 cm² ] = 9
Therefore,
Number of caps that can be formed = 9
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