Q
= 182 x 22/7 = 26 x 22 = 572 cm?
- A toy is in the form of a cone of radius 3.5 cm
mounted on a hemisphere of same radius. The
total height of the toy is 15.5 cm. Find the total
surface area of the toy.
Answers
EXPLANATION.
Question = 17 of image.
Toy is in the form of cone mount on hemisphere with same radius.
The diameter of conical part is = 6cm.
The height of conical part is = 4cm.
As we know that,
⇒ Radius of conical part = d/2 = 6/2 = 3cm.
Surface area of toy = Curved surface area of hemisphere + Curved surface area of cone.
⇒ Curved surface area of hemisphere = 2πr².
2 x 22/7 x 3 x 3 = 396/7cm².
⇒ Curved surface area of cone = πrl.
⇒ l = slant height.
⇒ l = √r² + h²
⇒ l = √(3)² + (4)².
⇒ l = √9 + 16.
⇒ l = √25.
⇒ l = 5cm.
Curved surface area of cone = 22/7 x 3 x 5 = 330/7cm².
Surface area of toy = 396/7cm² + 330/7cm².
Surface area of toy = 726/7cm² = 103.71cm².
Question of text writing.
A toy is in the form of cone of radius = 3.5cm.
It is mounted with hemisphere of same radius.
The total height of toy = 15.5cm.
As we know that,
Surface area of toy = Curved surface area of hemisphere + Curved surface area of cone.
⇒ Curved surface area of hemisphere = 2πr².
⇒ 2 x 22/7 x 3.5 x 3.5.
⇒ 2 x 22/7 x 35/10 x 35/10 = 77cm².
Curved surface area of cone = πrl
As we know that,
Height of cone = Total height of toy - radius of hemisphere.
Height of cone = 15.5 - 3.5. = 12cm.
⇒ l = slant height.
⇒ l = √h² + r².
⇒ l = √(12)² + (3.5)².
⇒ l = √144 + 12.25.
⇒ l = √156.25.
⇒ l = 25/2 = 12.5cm.
Curved surface area of cone = πrl.
⇒ 22/7 x 3.5 x 12.5 = 137.5cm².
Total surface area of toy = 77 + 137.5 = 214.5cm².