What is the maximum volume of the cylinder if the sum of its radius and the height is 8 cm?

=32π cu units.

What is the volume of the largest cone that can be inscribed in a hollow hemisphere of radius 7 cm?

R D Sharma – Mathematics 9 Height of cone will also be 7 cm. Hence, required volume of largest cone is 359.34 cm³.

What would the largest volume be if you were to inscribe a right circular cone into a sphere of radius r?

πR3 cubic units
Summary: The volume of the largest right circular cone that can be inscribed in a sphere of the radius R is (32/81)πR3 cubic units or (8/27) times the volume of the sphere.

How do you find the maximum volume of a cuboid?

Express the volume of the cuboid in terms of x. V=x2h=x2(75−x22x)=752x−12×3. Hence determine, as x varies, its maximum volume and show that this volume is a maximum. V′(x)=752−32×2.

How do you find the volume of a cylinder?

Multiply the area of the base by the height. You can think of the volume of the cylinder as the area of the base being extended throughout the height of the cylinder.

How do you calculate the surface area of a cylindrical container?

Let r be the radius & h be the height of the cylinder having its total surface area A (constant) since cylindrical container is closed at the top (circular) then its surface area (constant\\fixed) is given as = (area of lateral surface) + 2(area of circular top/bottom) A = 2πrh + 2πr2 h = A − 2πr2 2πr = A 2πr − r Now,…

What is the volume of a 2×4 cylinder?

You can think of the volume of the cylinder as the area of the base being extended throughout the height of the cylinder. Since you know that the area of the base is 3.14 in. 2 and that the height is 4 in., you can just multiply the two together to get the volume of the cylinder. 3.14 in. 2 x 4 in. = 12.56 in. 3 This is your final answer.

How do you find the size of a cardboard cylinder?

Enter the external radius of the cylinder. The standard is equal to approximately 5.5 cm. Determine the internal cylinder radius. It’s the internal radius of the cardboard part, around 2 cm. Find out what’s the height of the cylinder, for us it’s 9 cm.