Question

A can company makes a cylindrical can that has a radius of 6 cm and a height of 10 cm. One of the company’s clients needs a cylindrical can that has the same volume but is 15 cm tall. What must the new radius be to meet the client’s need? Round to the nearest tenth of a centimeter. 2.7 cm 4.9 cm 7.3 cm 24.0 cm

Answer 1

Answer: Second option is correct.

Explanation:

Since we have given that

Radius of cylinder (r)= 6 cm

Height of cylinder (h) = 10 cm

According to question, one of the company's clients needs a cylindrical can that has the same volume but is 15 cm tall.

So, Height of new cylinder (H)  = 15 cm

Radius of new cylinder = R cm

As we know the formula for " Volume of cylinder ":

$\pi r^2h=\pi R^2H\\\\6\times 6\times 10=R^2\times 15\\\\360=R^2\times 15\\\\\frac{360}{15}=R^2\\\\24=R^2\\\\\sqrt{24}=R\\\\4.9\ cm=R$

Hence, Second option is correct.

Answer 2

Answer:

4.9 cm

Step-by-step explanation:

Radius of cylindrical can = 6cm

Height of can = 10 cm

Volume of cylinder = $\pi r^{2} h$

                                = $\pi (6)^{2} \times 10$

                                = $360\pi$

Now, One of the company’s clients needs a cylindrical can that has the same volume but is 15 cm tall.

Volume of new cylinder with height 15 cm = $\pi r^{2} h$

                                                                      = $\pi r^{2} \times 15$

                                                                      = $15\pi r^{2}$

Since the volume of old can and new can should be same .

$360\pi =15\pi r^{2}$

$360 =15 r^{2}$

$\frac{360}{15} =r^{2}$

$24=r^{2}$

$\sqrt{24} =r$

$4.9 =r$

Thus the new radius be to meet the client’s need mus be 4.9 cm.