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 correct to two places of decimals. Also find the total surface area of the remaining solid.
(Take π = 3.1416).

Solution

Volume of the remaining solid Volume of the cylinder Volume of the cone

equals open square brackets straight pi space straight x space 6 squared space straight x space 8 minus 1 third straight x space straight pi space straight x space 6 squared space straight x 8 close square brackets space cm cubed equals space 2 over 3 space straight x space 3.1416 space straight x space 36 space straight x space 8 space cm cubed equals space 192 space straight x space 3.1416 space cm cubed equals space 603.1872 space cm cubed equals 603.19 space cm cubed

Slant height of the cone

AB thin space equals space square root of BC squared plus AC squared end root equals square root of left parenthesis 8 right parenthesis squared plus left parenthesis 6 right parenthesis squared end root equals square root of 64 plus 36 end root equals space 10 space cm

Now, total surface area of the remaining solid
= Curved surface area of the cylinder +
area of the base of the cylinder + curve
surface area of the cone
= (2 $straight pi$ x 6 x 8 + $straight pi$ x 6² + $straight pi$ x 6 x 10) cm²= (96 $straight pi$ + 36 $straight pi$ + 60 $straight pi$ ) cm²= 192 $straight pi$ 192 x 3.1416
= 603.1872 = 603.19 cm³

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Statistics

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 correct to two places of decimals. Also find the total surface area of the remaining solid.
(Take π = 3.1416).

Some More Questions From Statistics Chapter

2 cubes each of volume 64 cm³ are joined end to end. Find the surface area of the resulting cuboid.

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For Daily Free Study Material Join wiredfaculty

Statistics

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 correct to two places of decimals. Also find the total surface area of the remaining solid.(Take π = 3.1416).

Some More Questions From Statistics Chapter

2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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 correct to two places of decimals. Also find the total surface area of the remaining solid.
(Take π = 3.1416).

2 cubes each of volume 64 cm³ are joined end to end. Find the surface area of the resulting cuboid.