Question

A cone has base radius 5 cm and vertical height 10 correct to nearst cm. Calculate the maximum and minimum possible volumes of the cone, consistent with this data

Answer 1

Answer:4.5 ≤ r < 5.5 and 9.5 ≤ h < 10.5

V = πr²h

To get the minimum we use the lower bounds

so, V = π(4.5)²(9.5) => 604.4 cm³  

To get the maximum we use the upper bounds

so, V = π(5.5)²(10.5) => 997.8 cm³  

Note: the upper bounds are strictly 'less than', but for calculation purposes we use the values of r = 5.5 and h = 10.5

Step-by-step explanation:

Answer 2

Answer:

Minimum possible volume = 201 cm³

Maximum possible volume = 333 cm³

Step-by-step explanation:

Volume of cone formula = $\frac{1}{3}$$\pi$r²h

Minimum possible volume = $\frac{1}{3}$ × $\frac{22}{7}$ × (4.5)² × 9.5

                                            = 201 cm³

Maximum possible volume = $\frac{1}{3}$ × $\frac{22}{7}$ × (5.5)² × 10.5

                                            = 333 cm³