If two cubes of edge 5 cm each is joined end to end, find the surface area of the resulting cuboid

Try the new Google Books

Check out the new look and enjoy easier access to your favorite features

Derive the formula for the curved surface area and total surface area of the frustum of a cone, given to you in Section 13.5, using the symbols as explained.

Let h be the height, l the slant height and r1 and r2 the radii of the circular bases of the frustum ABB’ A’ shown in Fig. such that r1 > r2.
Let the height of the cone VAB be h1 and its slant height be i.e., VO = h1 and VA = VB = l1
∴ VA’ = VA – AA’ = l1– l
and VO’ = VO – OO’ = h1– hHere, ΔVOA ~ ΔVO‘A’

Now,Height of the cone VA‘B’

Let S denote the curved surface area of the frustum of cone. Then,S = Lateral (curved) surface area of cone VAB

- Curved surface area of cone VA‘B’

Curved surface area of the frustum
= π(r1 + r2)lTotal surface area of the frustum= Lateral (curved) surface area+ Surface area of circular bases

= π (r1 + r2) I + πr12 + πr22
= π {(r1 + r2) l + r12 + r22}.

>

Two cubes each of volume 125 cm3 are joined end to end to form a solid. Find the surface area of the resulting cuboid.

Solution

Volume of each cube = 125 cm3

So, edge of each cube = 5 cm

For new cuboid formed, l = 5+5 = 10 cm

b = 5 cm

h = 5 cm

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

= 2 (10 × 5 + 5 × 5 + 10 × 5) cm2

= 250cm2

Mathematics

Secondary School Mathematics X

Standard X