Robert Bosch Coordinate Geometry Quiz 4

The circumference of a circle is given by:
Circumference = 2 × π × Radius
Substitute the value:
30π cm = 2 × π × Radius
=> Radius = (30π cm) / (2 × π) = 15 cm

Now, Area of circle = πr²
= π × 15 × 15
= 225π cm².

Ans: 540 degrees
Explanation: The sum of the interior angles of any polygon is given by (n - 2) * 180 degrees, where n is the number of sides.
For a pentagon (5 sides), the sum of interior angles = (5 - 2) * 180 = 540 degrees. Therefore, the correct answer is (b) 540 degrees.

Ans: 8 cm
Explanation: In a right triangle, the Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. So, using the theorem: (length of other leg)^2 + 6^2 = 10^2. Solving for the length of the other leg: (length of other leg)^2 = 100 - 36 = 64. Taking the square root of 64, we get the length of the other leg = 8 cm. Therefore, the correct answer is (b) 8 cm.

Ans : 250π cubic units
Explanation: The volume of a cylinder is given by V = π * r^2 * h, where r is the radius and h is the height. Plugging in the given values: V = π * 5^2 * 10 = 250π cubic units. Therefore, the correct answer is (c) 250π cubic units.

Ans: 45 degrees
Explanation: Complementary angles add up to 90 degrees. If one angle is 45 degrees, the other angle must be 90 - 45 = 45 degrees.
Therefore, the correct answer is (a) 45 degrees.

Ans: 62 cm²
Explanation: The area of an equilateral triangle is given by A = (√3 / 4) * s^2, where s is the side length.
Plugging in the given value: A = (√3 / 4) * 12^2 = 36√3 cm².
Since √3 is approximately 1.732, the area is approximately
36 * 1.732 ≈ 62.352 cm².

Answer : 90 degrees
Explanation: The sum of the interior angles of a triangle is always 180 degrees. Therefore, the measure of the third angle = 180 - (30 + 60) = 90 degrees

Ans: 44 units
Explanation:
The circumference of a circle is given by C = π * d, where d is the diameter.
Plugging in the given value: C = 3.14 * 14 = 43.96 units.
Rounding to the nearest whole number, the circumference is approximately 44 units.

Ans : 144π
Solution:
Given: Diameter = 24 cm.
Hence, Radius, r = 12 cm
We know that the area of a circle = πr^2 square units.
If the diameter is 24, then radius will be = 12 cm
A = π(12)^2 cm2
A = 144π cm2
Hence, the area of a circle whose diameter is 24 cm = 144π cm2.

Ans: 65π cm²
Explanation:
The lateral surface area of a right circular cone is given by π * r * l,
where "r" is the base radius and "l" is the slant height.
Plugging in the given values:
Lateral Surface Area = π * 5 * 13 = 65π cm².