Question

hi there

1) The shape of solid iron rod is a cylindrical. Its height is 11 cm. and base diameter is 7 cm. Then find the total volume of 50 such rods?

2) A toy is in the form of a cone mounted on a hemisphere. The diameter of the base and the height of the cone are 6 cm and 4 cm respectively. Determine the surface area of the toy.
(use π = 3.14)

Answer 1

$\sf{ \green{ \underline{ \tiny{The \: shape \: of \: solid \: iron \: rod \: is \: a \: cylindrical. \: Its \: height \: is \: 11 \: cm. \: and \: base}}}} \\ \sf{ \red{ \tiny{ \underline{diameter \: is \: 7 cm. Then \: find \: the \: total \: volume \: of \: 50 \: such \: rod}}}}$

▶ Solution : ▶

It is Given that shape of solid iron rod is a cylindrical. Its height is 11 cm. and base diameter is 7 cm.

So , We have!

↪ Height of Cylinder ( Rod) = 11 Cm

↪ Base Diameter of Cylinder ( Rod ) = 7 ÷ 2 cm

▶ To Find : Find the Volume of 1 Rod ?

↪ Volume of Cylinder = πr²h

↪ Volume of Cylinder = 22/7 × (7/2)² × (7/2)² × 11

↪Volume of Cylinder = 22×7×49/4 × 49/4 × 11

↪Volume of Cylinder = 847/2 cm²

▶ According to the Question's Statement!

↪ VOLUME OF 50 ROD = 50 × ( Volume of 1 Rod)

↪ VOLUME OF ROD = 50 × 847/2 cm²

↪ Volume of Rod = 847 × 25cm²

↪ Volume of Rod = 21,175 cm²

➡Therefore, Required Volume of 50 ROD is 21,175cm² ↙

$\sf{ \red{ \underline{ \tiny{ 2) A \: toy \: is \: in \: the \: form \: of \: a \: cone \: mounted \: on \: a \: hemisphere. \: The \: diameter \: of \: the \: base}}}} \: \: \\ \sf{ \green{ \underline{ \tiny{and \: the \: height \: of \: the \: cone \: are \: 6 cm \: and \: 4 cm \: respectively. }}}} \\ \sf{ \blue{ \underline{ \tiny{ Determine \: the \: \: surface \: area \: of \: the \: toy.}}}}$

▶ Method of Solution : ▶

in this Question, It is given that A toy is in the form of a cone mounted on a hemisphere. The diameter of the base and the height of the cone are 6 cm and 4 cm respectively.

We have Need to Find the slant Height of Cone!

↪ Slant height of cone = √(3)²+ (4)²

 = √9 + 16

= √25

= 5 cm

Now, According to the Question's Statement!

↪ Statement : Determine the surface area of the toy.

[TSA of toy = CSA of cone + CSA of hemisphere]

➡ πrl + 2πr²

↪ rl + 2r²

↪ r [ l + 2r ]

↪ 3.14 × 3 [ 5 + 2 (3) ]

↪3.14 × 3 [5 + 6]

↪ 3.14 × 3 × 11

↪726 ÷ 33

↪ 103.71 cm²

▶ Hence, Required SURFACE AREA OF THE TOY is (103.71 cm²) ▶

Answer 2

in this Question, It is given that A toy is in the form of a cone mounted on a hemisphere. The diameter of the base and the height of the cone are 6 cm and 4 cm respectively.

We have Need to Find the slant Height of Cone!

↪ Slant height of cone = √(3)²+ (4)²

= √9 + 16

= √25

= 5 cm

Now, According to the Question's Statement!

↪ Statement : Determine the surface area of the toy.

[TSA of toy = CSA of cone + CSA of hemisphere]

➡ πrl + 2πr²

↪ rl + 2r²

↪ r [ l + 2r ]

↪ 3.14 × 3 [ 5 + 2 (3) ]

↪3.14 × 3 [5 + 6]

↪ 3.14 × 3 × 11

↪726 ÷ 33

↪ 103.71 cm²

▶ Hence, Required SURFACE AREA OF THE TOY is (103.71 cm²)