Name: Mensuration Formulas
Uploaded: 2019-07-19
Duration: 10 min 20 s
Description: Various mensuration formula is covered in geometry useful for the exam point. In order to excel in this topic, you must know the formulas and concepts used t...

Question

From a solid cylinder whose height is

8 cm

and radius

6 cm

, a conical cavity of height

8 cm

and of base radius

6 cm

is hollowed out. Find the Volume of the remaining solid.Also, find the total surface area of the remaining solid.(Take

π = 3.14

)

Accepted Answer

Radius of a solid cylinder $= 6 cm$

Height of a solid cylinder $= 8 cm$

We know that the volume of a cylinder $= {πr}^{2} h$

Volume of a cylinder $= 3.14 \times 36 \times 8 = 904.32 {cm}^{3}$

We know that, the volume of a cone $= \frac{1}{3} {πr}^{2} h$

Volume of a cone $= \frac{1}{3} \times 3.14 \times 36 \times 8 = 301.44 {cm}^{3}$

Volume of the remaining solid $=$ Volume of a cylinder $-$ Volume of a cone

$= 904.32 - 301.44 = 602.88 {cm}^{3}$

Hence, the volume of the remaining solid is $602.88 {cm}^{3}$

We know that, the curved surface area of a cylinder $= 2 πrh$

Curved surface area of a cylinder $= 2 \times 3.14 \times 8 \times 6 = 96 \times 3.14 = 301.44 {cm}^{2}$

We know that the Base Area of a cylinder $= {πr}^{2}$

Base area $= 3.14 \times 36 = 113.04 {cm}^{2}$

We know that, the lateral surface area of a cone $= πr l$

Slant height of the cone, $l = \sqrt{r^{2} + h^{2}} = \sqrt{36 + 64} = 10 cm$

Lateral surface area of a cone $= 3.14 \times 6 \times 10 = 188.4 {cm}^{2}$

Total surface area of the remaining solid $=$ Curved surface area of cylinder $+$ Base area of cylinder $+$ Curves surface area of cone

$= 188.4 + 113.04 + 301.44 = 602.88 {cm}^{2}$

Hence, the total surface area of the remaining solid is $602.88 {cm}^{2}$

From a solid cylinder whose height is $8 cm$ and radius $6 cm$ , a conical cavity of height $8 cm$ and of base radius $6 cm$ is hollowed out. Find the Volume of the remaining solid.Also, find the total surface area of the remaining solid.(Take $π = 3.14$ )

Important Questions on Surface Areas and Volumes

Learn and Prepare for any exam you want !

From a solid cylinder whose height is 8 cm and radius 6 cm, a conical cavity of height 8 cm and of base radius 6 cm is hollowed out. Find the Volume of the remaining solid.Also, find the total surface area of the remaining solid.(Take π=3.14)

Important Questions on Surface Areas and Volumes

Learn and Prepare for any exam you want !

From a solid cylinder whose height is $8 cm$ and radius $6 cm$ , a conical cavity of height $8 cm$ and of base radius $6 cm$ is hollowed out. Find the Volume of the remaining solid.Also, find the total surface area of the remaining solid.(Take $π = 3.14$ )