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Home » 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.
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.
CBSE | Class 10 | Exercise 13.1 | Maths | NCERT | Surface Areas And Volumes
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.

The chart is as per the following:

Ncert solutions class 10 chapter 13-3

Considering that the sweep of the cone and the side of the equator (r) = 3.5 cm or 7/2 cm

The complete stature of the toy is given as 15.5 cm.

Thus, the stature of the cone (h) =

    \[15.5-3.5\text{ }=\text{ }12\text{ }cm\]

Ncert solutions class 10 chapter 13-4

∴ The bended surface space of cone = πrl

    \[\left( 22/7 \right)\times \left( 7/2 \right)\times \left( 25/2 \right)\text{ }=\text{ }275/2\text{ }cm2\]

Additionally, the bended surface space of the side of the equator = 2πr2

    \[2\times \left( 22/7 \right)\times \left( 7/2 \right)2\]

    \[=\text{ }77\text{ }cm2\]

Presently, the Total surface space of the toy = CSA of cone + CSA of half of the globe

    \[=\text{ }\left( 275/2 \right)+77\text{ }cm2\]

    \[=\text{ }\left( 275+154 \right)/2\text{ }cm2\]

    \[=\text{ }429/2\text{ }cm2\text{ }=\text{ }214.5cm2\]

Thus, the all out surface region (TSA) of the toy is 214.5cm2

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