Class 10th, Surface Area and Volume, Exe-13.1 (Solution)

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Maths NCERT Class 10th Chapter 13 – Surface Area and Volume

 Class 10th, Maths, Exercise: 13.1 (Q1 to Q4)

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Q1:- 2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.

Answer:

The diagram

Given,

The Volume (V) of each cube is = 64 cm3

This implies that a3 = 64 cm3

∴ a = 4 cm

Now, the side of the cube = a = 4 cm

Also, the length and breadth of the resulting cuboid will be 4 cm each. While its height will be 8 cm.

So, the surface area of the cuboid = 2(lb + bh + lh)

= 2(8×4 + 4×4 + 4×8) cm2

= 2(32 + 16 + 32) cm2

= (2 × 80) cm2 = 160 cm2

Q2:- A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.

Answer:

The diagram 

Now, the given parameters are:

The diameter of the hemisphere = D = 14 cm

The radius of the hemisphere = r = 7 cm

Also, the height of the cylinder = h = (13 – 7) = 6 cm

And, the radius of the hollow hemisphere = 7 cm

Now, the inner surface area of the vessel = CSA of the cylindrical part + CSA of hemispherical part

=> (2πrh+2πr2) cm2 = 2πr(h+r) cm2

=> 2 × 22/7 × 7 (6+7) cm2 = 572 cm2

Q3:-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.

Answer:

The diagram 

Given that the radius of the cone and the hemisphere (r) = 3.5 cm or 7/2 cm

The total height of the toy is given as 15.5 cm.

So, the height of the cone (h) = 15.5 – 3.5 = 12 cm

∴ The curved surface area of cone = πrl

=> (22/7 × 7/2 × 25/2) = 275/2 cm2

Also, the curved surface area of the hemisphere = 2πr2

=> 2 × 22/7 × (7/2)2

= 77 cm2

Now, the Total surface area of the toy = CSA of cone + CSA of hemisphere

= (275/2 + 77) cm2

= (275+154)/2 cm2

= 429/2 cm2 = 214.5 cm2

So, the total surface area (TSA) of the toy is 214.5 cm2

Q4:- A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.

Answer:

It is given that each side of cube is 7 cm. So, the radius will be 7/2 cm.

The Diagram

We know,

The total surface area of solid (TSA) = surface area of cubical block + CSA of hemisphere – Area of base of hemisphere

∴ TSA of solid = 6×(side)2 + 2πr2 – πr2

= 6×(side)2 + πr2

= 6×(7)2 + (22/7 × 7/2 × 7/2)

= (6×49) + (77/2)

= 294 + 38.5 = 332.5 cm2

So, the surface area of the solid is 332.5 cm2

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