State whether the following statement is true or false:
The radius of a cone can be $3 \, cm$,slant height $4 \, cm$,and height $5 \, cm$.
The radius of a cone can be $3 \, cm$,slant height $4 \, cm$,and height $5 \, cm$.
(B) The statement is False.
In a right circular cone,the radius $(r)$,height $(h)$,and slant height $(l)$ form a right-angled triangle where the slant height is the hypotenuse.
According to the Pythagorean theorem,the relationship is $l^2 = r^2 + h^2$.
Given: $r = 3 \, cm$,$h = 5 \, cm$,and $l = 4 \, cm$.
Calculating $r^2 + h^2 = 3^2 + 5^2 = 9 + 25 = 34$.
Calculating $l^2 = 4^2 = 16$.
Since $16 \neq 34$,the given dimensions cannot form a right circular cone because the slant height must be the longest side of the right-angled triangle formed by the radius and the height.
In a right circular cone,the radius $(r)$,height $(h)$,and slant height $(l)$ form a right-angled triangle where the slant height is the hypotenuse.
According to the Pythagorean theorem,the relationship is $l^2 = r^2 + h^2$.
Given: $r = 3 \, cm$,$h = 5 \, cm$,and $l = 4 \, cm$.
Calculating $r^2 + h^2 = 3^2 + 5^2 = 9 + 25 = 34$.
Calculating $l^2 = 4^2 = 16$.
Since $16 \neq 34$,the given dimensions cannot form a right circular cone because the slant height must be the longest side of the right-angled triangle formed by the radius and the height.
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