Surface Areas and Volumes Class 10 Formulas PDF

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In this article, we are going to discuss the surface area and volume of different solid shapes such as the cube, cuboid, cone, cylinder, etc. The surface area can be generally classified into Lateral Surface Area (LSA), Total Surface Area (TSA), and Curved Surface Area (CSA). Here you can also know about the procedure to find the volume and its surface area in detail.

Surface Areas and Volumes Class 10 Formulas PDF

Below given is the table for the calculating Surface area and Volume for the basic geometrical figures:

Surface Areas and Volumes Class 10 Formulas – Solved Examples

Q.1. What is the curved surface area of a hemisphere if the diameter is 12cm. 12cm.

Ans: The diameter is 12cm.12cm.

The radius is 122cm=6cm122cm=6cm

The curved surface area of the hemisphere =2πr2=2×227×6×6cm2=2πr2=2×227×6×6cm2

=226.28cm2=226.28cm2

Q.2. Find the length of the sides of the cube if its volume is 216cm3.216cm3.

Ans: Given, the volume of the cube =216cm3=216cm3

Let the length of the sides is a.a.

We know,

The volume of a cube =(side)3=(side)3

Substituting the value we get,

a3=216a3=216

⇒a=216−−−√3⇒a=6cm⇒a=2163⇒a=6cm

Hence, the side of the cube is 6cm.6cm.

Q.3. If the diagonal is 43–√cm.43cm. Find the volume of the cube.

Ans: We know, V=d333√⇒V=(43√)333√=64×33√33√⇒V=64cm3V=d333⇒V=(43)333=64×3333⇒V=64cm3

Hence, the volume of the cube is 64cm3.64cm3.

Q.4. The slant height of a frustum of a cone is 4cm,4cm, and the perimeters (circumference) of its circular ends are 18cm18cm and 6cm.6cm. Find the curved surface area of the frustum.

Ans: Given, l=4cml=4cm

Circumference of a circular end =18cm=18cm

⇒2πr1=18cm⇒2πr1=18cm

⇒πr1=9cm⇒πr1=9cm

Circumference of another circular end =6cm=6cm

⇒2πr2=6cm⇒2πr2=6cm

⇒πr2=3cm⇒πr2=3cm

We know that curved surface area =πl(r1+r2)=l(πr1+πr2)=πl(r1+r2)=l(πr1+πr2)

=4×(9+3)cm2=4×(9+3)cm2

=48cm2=48cm2

Hence, the curved surface area of the frustum is 48cm2.48cm2.

Q.5. Madhu prepares a birthday cap with a piece of paper in the form of a right circular cone of radius 33 inches and a height of 44 inches. Find the slant height of the birthday cap made by her.

Ans: Given that, the birthday cap prepared by Madhu is in the shape of a right circular cone.

The radius of the cone (r)=3(r)=3 inches and the height of the cone (h)=4(h)=4 inches.

It is known that the slant height of the cone is given by l=r2+h2−−−−−−√.l=r2+h2.

⇒l=32+42−−−−−−√⇒l=32+42

⇒l=9+16−−−−−√⇒l=9+16

⇒l=25−−√=5⇒l=25=5 inches

Hence, the slant height of the birthday cap is 55 inches.

You can download Surface Areas and Volumes Class 10 Formulas PDF by clicking on the following download link.