The sum of the areas of the 10 squares,the le | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The sum of the areas of the squares is given by the sum of the squares of their side lengths:Sum $= 20^2 + 21^2 + \ldots + 29^2$Using the formula

Vedclass · Accepted Answer

$6085$

Vedclass · Answer

(A) The sum of the areas of the squares is given by the sum of the squares of their side lengths:Sum $= 20^2 + 21^2 + \ldots + 29^2$Using the formula for the sum of squares of the first $n$ natural numbers,$\sum_{k=1}^{n} k^2 = \frac{n(n+1)(2n+1)}{6}$,we can write:Sum $= \sum_{k=1}^{29} k^2 - \sum_{k=1}^{19} k^2$$= \frac{29(29+1)(2 	imes 29 + 1)}{6} - \frac{19(19+1)(2 	imes 19 + 1)}{6}$$= \frac{29 	imes 30 	imes 59}{6} - \frac{19 	imes 20 	imes 39}{6}$$= (29 	imes 5 	imes 59) - (19 	imes 10 	imes 13)$$= 8555 - 2470 = 6085 \, cm^2$.

The sum of the areas of the $10$ squares,the lengths of whose sides are $20 \, cm, 21 \, cm, \ldots, 29 \, cm$ respectively is ...... $cm^2$.

Similar Questions

$A$ solid metallic sphere of radius $21\, cm$ is melted and recast into a cone with diameter of the base as $21\, cm$. What is the height (in $cm$) of the cone?

$A$ lawn is in the form of a rectangle having its breadth and length in the ratio $3:4$. The area of the lawn is $\frac{1}{12}$ hectare. The breadth of the lawn is..........$metres$.

$A$ circle and a rectangle have the same perimeter. The sides of the rectangle are $18 \text{ cm}$ and $26 \text{ cm}$. The area of the circle is .......... $\text{cm}^2$. [Take $\pi = \frac{22}{7}$]

If the length of a rectangle is increased by $10 \%$ and its breadth is decreased by $10 \%,$ then its area

One of the diagonals of a rhombus is double the other diagonal. Its area is $25\, cm^{2}$. The sum of the diagonals is.......$cm$

Vedclass Test Series

Exam Paper Generator

Online Exam Module