Question

From a cylindrical objects of diameter 70cm and height 84cm a right solid cone having its base as one of the circular ends of the cylinder and height 84cm is removed calculate the volume of the remaining solid object leaving your answer in standard form

Answer 1

The volume of the remaining solid object is equal to 215,600 cm³.

Given:

Diameter of the cylinder (d) = 70 cm

Height of the cylinder (H) = 84 cm

Height of the cone (h) = 84 cm

To Find:

The volume of the remaining solid object.

Solution:

→ The radius of a circular base is equal to half of the diameter of the circular base.

∵ The diameter (d) of the cylinder is equal to 70 cm.

∴ The radius (r) of the cylinder would be equal to 35 cm.

→ The volume (V) of a cylinder is given as: $V=\pi r^{2} H$

→ Here 'H' is equal to the height of the cylinder and 'r' is equal to the radius of the cylinder.

 $\therefore The \:volume\:of\:the\:given\:cylinder=\pi r^{2}H=\frac{22}{7}\times(35)^{2}\times84 \\\\\therefore The \:volume\:of\:the\:given\:cylinder=323,400\:cm^{3}$

→ The base of the cone as well as cylinder are the same.

∴ The radius (r) of the cone would be equal to 35 cm.

→ The volume (V) of a cone is given as:  $V=\frac{1}{3} \pi r^{2} h$

→ Here 'h' is equal to the height of the cone and 'r' is equal to the radius of the cone.

  $\therefore The \:volume\:of\:the\:given\:cone=\frac{1}{3} \pi r^{2}h=\frac{1}{3} \times\frac{22}{7}\times(35)^{2}\times84 \\\\\therefore The \:volume\:of\:the\:given\:cone=107,800\:cm^{3}$

→ Therefore the volume of the remaining solid object would be equal to the Volume of the cylinder minus the volume of the cone.

 $\therefore Volume\:of\:the\:remaining\:solid =Volume\:of\:Cylinder- Volume\:of\:Cone$

  ∴ Volume of the remaining solid = 323,400 - 107,800 = 215,600 cm³

Therefore the volume of the remaining solid object would be equal to 215,600 cm³.

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