To have a surface area of 9π square units of a ball, what should be the diameter (in units) of the ball?
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The surface area of a sphere is given by the formula: 4πr², where r is the radius of the sphere.
We are given the surface area as 9π. So, set the formula equal to 9π:
4πr² = 9π
Divide both sides by π:
4r² = 9
Now, divide by 4:
r² = 9/4
Take the square root of both sides:
r = √(9/4) = 3/2 = 1.5 units.
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Important Questions from Geometry
In a circle with center O, an arc ABC subtends an angle of 138° at the centre of the circle. The chord AB is produced to a point P. Then, the measure of ∠CBP is:
A secant PAB is drawn from an external point P to the circle with the centre at O, intersecting it at A and B. If OP = 17 cm, PA = 12 cm and PB = 22.5 cm, then the radius of the circle is:
In △ABC, the internal bisectors of ∠B and ∠C meet at O. If ∠BAC = 72°, then the value of ∠BOC is:
The side BC of △ABC is produced to a point D. If AC = BC and ∠BAC = 70°, then find the value of 2.5∠ACD – 1.5∠ABC.
If the radius and height of a right circular cylinder are 21 cm and 5 cm, respectively, then the total surface area of the cylinder is (use π = 22 / 7):
