Class |
10 |

Chapter |
Surface Areas and Volumes |

Subject |
Math |

Category |
Important Question Answer |

**Class 10 Math Chapter 12 Important Question Answer**

**Q1. From a solid cylinder whose height is 2.4cm and diameter 1.4cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm ^{2}.**

**Ans**.

Given, Radius of cylinder r = cm,

Height of cylinder, h = 2.4 cm

Radius of cone, r = 0.7 cm

Height of cone, h = 2.4 cm

Slant height of the conical cavity (l) =

=

= 2.5 cm

Total surface are of the remaining solid

= Surface area of conical cavity + TSA of the cylinder

= πrl + 2πr(r + h)

= πr(l + 2h + r)

=

= 17.6 cm^{2}

**Q2. Two cubes each of volume 64 cm ^{3} are joined end to end. Find the surface area of the resulting cuboid. Most Important**

**Ans**.

Volume of each cube = 64 cm^{3}

It means a^{3} = 64

a = 4 cm

Now, the side of cube, a = 4 cm

Also, the length of resulting cuboid is 8 cm and breadth and height is 4 cm each.

Therefore, the surface area of resulting cuboid = 2(lb + bh + hl)

= 2(8×4 + 4×4 + 4×8)

= 2(32 + 16 + 32)

= 160 cm^{2}

**Q****3****. A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and total height of the vessel is 13 cm. Find the inner surface area of the vessel.**

**Ans**.

Given, diameter of hemisphere = 14cm

Therefore, radius of hemisphere will be 7 cm.

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

Radius of the hollow hemisphere = 7 cm

Now, The Inner surface area of the vessel = CSA of the cylinder + CSA of Hemisphere

= 2πrh + 2πr^{2}

= 2πr(h + r)

=

= 2×22×13

= 572 cm^{2}

**Q****4****. A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. The total height of the toy is 15.5 cm. Find the total surface area of the toy.**

**Ans**.

Given, radius of hemisphere = 3.5 cm

Surface area of the hemisphere = 2πr^{2}

= = 77 cm^{2}

Height of conical part = 15.5 cm – 3.5 cm = 12 cm

Radius of conical part = 3.5 cm

Slant height of conical part (l) =

= = 12.5 cm

Curved surface area of conical part = πrl = = 11×12.5 = 137.5 cm^{2}

Total surface area of the toy = Surface area of hemisphere + Surface area of conical part

= 77 cm^{2} + 137.5 cm^{2}

= 214.5 cm^{2}

**Q****5****. 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 solid.**

**Ans**.

Given, each side of cube = 7 cm. So, the radius of hemisphere will be 7/2 cm.

Total surface of the solid

= Total Surface area of cube + CSA of hemisphere – Area of base of hemisphere

= 6(side)^{2} + 2πr^{2} – πr^{2}

= 6(side)^{2} + πr^{2}

= 6(7)^{2} +

= 294 +

= 294 + 38.5 = 332.5 cm^{2}

**Q****6****. A medicine capsule is in the shape of a cylinder with two hemisphere struck to each of its ends. The length of entire capsule is 14 mm and diameters of the capsule is 5 mm. Find its surface area.**

**Ans**.

Given, diameter of capsule = 5 mm.

Therefore, radius of capsule = 5/2 = 2.5 mm

Length of the capsule = 14 mm

Length of the cylinder = 14 – (2.5 + 2.5) = 9 mm

Curved Surface area of a hemisphere = 2πr^{2} = = mm^{2}

Now, the Curved surface area of cylinder = 2πrh = mm^{2}

The required surface area of the medicine capsule = 2(surface area of hemisphere) + curved surface area of cylinder

= mm^{2}

**Q****7****. Write the formula for finding out the curved surface area of the cylinder.**

**Ans**. Curved surface area of cylinder = 2πrh

where r is the radius of base and h is the height of cylinder.

**Q****8****. An underground water tank is in the form of a cuboid of edges 48 m, 36 m and 28m. Find the volume of the tank.**

**Ans**. Dimensions of cuboidal water tank are 48m, 36m and 28m.

Therefore,

Volume of cuboid tank = lbh

= 48 × 36 × 28

= 48,384 m^{3}

**Q****9****. The volume of the right circular cone of height 21 cm and radius of its base 5 cm, is, _________.**

**Ans**. Given r = 5 cm, h = 21 cm

Volume of right circular cone = πr^{2}h

=

= 1650 cm^{2}

**Q1****0****. Find the volume of the cone of height 24 cm and radius of base 6 cm.**

** Ans**. Given r = 6 cm and h = 24 cm

Using, Volume of Cone = πr^{2}h

= × ×6×6×24 = cm^{3}

Therefore, required volume of cone is cm^{3}

**Q1****1****. The volume of the sphere of radius 8 cm is _________.**

**Ans**. radius of sphere r = 8 cm

Volume of sphere = πr^{3} = ××8×8×8 = cm^{3}

Also Read |
Class 10 Math NCERT Solution |

Also Read |
Class 10 Important Questions [Latest] |