The circumference of the base of a solid right circular cylinder is 88 cm and its height is 150 cm. What is the volume (in cm3) of the cylinder?
92400
The problem requires us to find the volume of a solid right circular cylinder using the given data. Here's the step-by-step solution:
The circumference of the base of the cylinder is provided as 88 cm. The formula for the circumference \(C\) of the base of the cylinder (which is a circle) is given by:
\(C = 2 \pi r\)
where \(r\) is the radius of the base.
Substituting the given circumference, we can solve for \(r\):
\(88 = 2 \pi r\)
\(r = \frac{88}{2 \pi} = \frac{44}{\pi}\)
The height \(h\) of the cylinder is given as 150 cm.
The volume \(V\) of a cylinder is calculated using the formula:
\(V = \pi r^2 h\)
Substituting the values of \(r\) and \(h\) we found:
\(V = \pi \left(\frac{44}{\pi}\right)^2 \times 150\)
Simplifying further:
\(V = \frac{1936 \times 150}{\pi}\)
Approximating \(\pi \approx 3.14\):
\(V = \frac{290400}{3.14} \approx 92400\)
Thus, the volume of the cylinder is approximately \(92400 \, \text{cm}^3\), which matches the correct answer provided in the options.
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Important Questions from 3-D Mensuration
- Find the surface area of a sphere whose diameter is equal to 98 cm.
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- The volume of a solid cylinder is 5852 cm³ and its height is 38 cm. What is the total surface area of the solid cylinder? (Round your answer to the nearest integer) (Use $\pi = \frac{22}{7}$)
