The volume of a cylinder with base radius 3 cm and height 6 cm is
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Ada is <u>incorrect</u>, as the length of diagonal SQ is not two times the length of diagonal OM. The theorem used is the Pythagoras Theorem.
For Rectangle PQRS:-
By Pythagoras Theorem, in right triangle PQS,
SQ² = PQ² + PS²,
or, SQ² = 8² + 16² sq. inches,
or, SQ² = 64 + 256 sq. inches,
or, SQ = √320 sq. inches,
or, SQ = 8√5 inches.
Thus, the length of diagonal SQ, of rectangle PQRS is 8√5 inches.
For Square LMNO:-
By Pythagoras Theorem, in right triangle LMO,
OM² = LM² + LO²,
or, OM² = 8² + 8² sq. inches,
or, OM² = 64 + 64 sq. inches,
or, OM = √128 sq. inches,
or, OM = 8√2 inches.
Thus, the length of diagonal OM, of square LMNO is 8√2 inches.
We know that 2*OM ≠ SQ, as 2*8√2 ≈ 8√5.
Thus, Ada is <u>incorrect</u>, as the length of diagonal SQ is not two times the length of diagonal OM. The theorem used is the Pythagoras Theorem.
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<span>Given that the railroad rail is 6 kilometers before expansion.
When the railroad expands, it makes an isosceles triangle at the center of the rail.
The base of the triangle is 6 kilometers while each leg of the triangle is given by (6 + 10/100,000) / 2 = 6.0001 / 2 = 3.00005 kilometers.
[recall that 100,000 centimeters gives 1 kilometers, thus 10 centimetres gives 10/100,000 kilometers]
Taking one half of the isoceles triangle, we have a right triangle with one of the leg as 6 / 2 = 3 kilometers and the hypothenus = 3.00005 kilometers.
Thus, using the Pythagoras theorem, we find the other leg (height) of the right triangle as follows.
Let the other leg of the right triangle be h, then
Thus, the center of the rail will rise 0.01732058 kilometers above the ground.
But, there are 1,000 meters in 1 kilometers, therefore, </span><span><span>the center of the rail will rise 0.01732058 x 1,000 = 17.32 meters above the ground.</span></span>
When the railroad expands, it makes an isosceles triangle at the center of the rail.
The base of the triangle is 6 kilometers while each leg of the triangle is given by (6 + 10/100,000) / 2 = 6.0001 / 2 = 3.00005 kilometers.
[recall that 100,000 centimeters gives 1 kilometers, thus 10 centimetres gives 10/100,000 kilometers]
Taking one half of the isoceles triangle, we have a right triangle with one of the leg as 6 / 2 = 3 kilometers and the hypothenus = 3.00005 kilometers.
Thus, using the Pythagoras theorem, we find the other leg (height) of the right triangle as follows.
Let the other leg of the right triangle be h, then
Thus, the center of the rail will rise 0.01732058 kilometers above the ground.
But, there are 1,000 meters in 1 kilometers, therefore, </span><span><span>the center of the rail will rise 0.01732058 x 1,000 = 17.32 meters above the ground.</span></span>