The ratio between the radius of the base and the height of a cylinder is 3:4. If its volume is 38,808 cm³, then using \( \pi = \frac{22}{7} \), find the diameter of the cylinder.
42 cm
Let the radius of the base be \(3x\) and the height be \(4x\).
The volume of a cylinder is given by:
\[ V = \pi r^2 h \]
Substituting the given values:
\[ \frac{22}{7} \times (3x)^2 \times 4x = 38,808 \] \[ \frac{22}{7} \times 9x^2 \times 4x = 38,808 \] \[ \frac{22}{7} \times 36x^3 = 38,808 \] \[ \frac{792x^3}{7} = 38,808 \] \[ 792x^3 = 271,656 \] \[ x^3 = 343 \] \[ x = 7 \]
Thus, the radius of the cylinder is:
\[ 3x = 3 \times 7 = 21 \text{ cm} \]
Diameter = \( 2 \times 21 = 42 \) cm.
Thus, the correct answer is 42 cm.
Important Questions from Co-ordinate Geometry
In which quadrant is the point (–4, –3) located?
A. I
B. II
C. III
D. IV
The area of a quadrilateral whose vertices are (3,0), (4,5), (-1,4) and (-2,-1) taken in order, is:
The coordinates of a point A, where AB is the diameter of a circle whose centre is (2, -3) and B is (1, 4) is:
The ratio between the radius of the base and the height of a cylinder is 3:4. If its volume is 38,808 cm³, then using \( \pi = \frac{22}{7} \), find the diameter of the cylinder.
In ΔABC if ∠A = 50° and ∠B = 70°, find the measure of exterior angle A.
