CLASS 07
Practice Questions Maths
1. A gardener wants to fence a circular garden of diameter 21 m. Find the
length of the rope he needs to purchase if he makes 2 rounds of fence.
Also find the cost of the rope, if it cost 4 per meter. (Take π = 22/7)
2. Shazli took a wire of length 44 cm and bent into the shape of a circle. Find
the radius of that circle. Also, find the area. Of the same wire is bent into
the shape of a square, what will be the length of each of its side? Which
figure encloses more area, the circle or the square? (Take π = 22/7)
3. Ratio of the area of ∆ WXY to the area of ∆ WZY is 3 : 4. If the
area of ∆ WXZ is 56 cm2 and WY = 8 cm, find the lengths of XY and YZ.
4. In the given figure, ABCD is a parallelogram, in which
AB = 8 cm, AD = 6 cm and altitude AE = 4 cm. Find the
altitude corresponding to side AD.
5. A rectangular shaped swimming pool with dimensions 30 m × 20 m has 5
m wide cemented path along its length and 8 m wide path along its width
(as shown in figure). Find the cost of cementing the path at the rate of Rs
200 per m².
6. The perimeter of a rectangle is 40 m. Its length is four metres less
than five times its breadth. Find the area of the rectangle.
7. A wall of a room is of dimensions 5 m × 4 m. It has a window of
dimensions 1.5 m × 1m and a door of dimensions 2.25 m × 1m.
Find the area of the wall which is to be painted.
8. In the given triangles below, perimeter of ∆ABC = perimeter of
∆PQR. Find the area of ∆ABC.
9. In the below figure, area of ∆PQR is 20 cm² and area of ∆PQS is 44 cm².
Find the length RS, if PQ is perpendicular to QS and QR is 5cm.
10. Area of a triangle PQR right-angled at Q is 60 cm². If the
smallest side is 8cm long, find the length of the other two sides.
11. A table cover of dimensions 3 m 25 cm × 2 m 30 cm is spread on a
table. If 30 cm of the table cover is hanging all around the table, find
the area of the table cover which is hanging outside the top of the
table. Also find the cost of polishing the table top at Rs.16 per square
metre.
12. The dimensions of a plot are 200 m × 150 m. A builder builds 3
roads which are 3 m wide along the length on either side and one in
the middle. On either side of the middle road he builds houses to
sell. How much area did he get for building the houses?
13. A room is 4.5 m long and 4 m wide. The floor of the room is to be
covered with tiles of size 15 cm by 10 cm. Find the cost of covering
the floor with tiles at the rate of Rs. 4.50 per tile.
14. Find the total cost of wooden fencing around a circular garden of
diameter 28 m, if 1m of fencing costs Rs. 300.
15. Priyanka took a wire and bent it to form a circle of radius 14 cm.
16. Then she bent it into a rectangle with one side 24 cm long. What is
the length of the wire? Which figure encloses more area, the circle or
the rectangle?
17. How much distance, in metres, a wheel of 25 cm radius will cover if
it rotates 350 times?
18. A circular pond is surrounded by a 2 m wide circular path. If outer
circumference of circular path is 44 m, find the inner circumference
of the circular path. Also find area of the path.
19. Dimensions of a painting are 60 cm × 38 cm. Find the area of the wooden
frame of width 6 cm around the painting as shown in below figure.
Case Based Questions
1. Given below is the map of a society park:
The park has four grass patches of equal area. The dotted line represents the
path for running and jogging.
(i) What is the perimeter of grass patch 1 ?
(a) 191 m (b) 382 m (c) 800 m (d) 1528 m
(ii) What is the area of the running and jogging path?
(a) 3519 m² (b) 3600 m² (c) 8495.25 m² (d) 37500 m²
(iii) Two sitting benches are installed in the grass patches. The seat of each bench
is of the length 1.2 m and width 0.7 m . How much area (in) is reserved for sitting
in the park?
(a) 0.84 (b) 1.68 (c) 3.36 (d) 6.72
(iv) The patch 2 is divided diagonally into two triangles of equal areas. Tulips are
planted in one triangular area. What is the area in which the tulips are planted?
(a) 2831.75 m² (c) 4247.625 m²
(b) 8495.25 m² (d) 18750 m²
2. Bacteria can divide every 15 minutes. So one bacterium can multiply to 2 in
30 minutes, 4 in 45 minutes and so on.
(i) How many bacteria will be there in 4 hours.
(a) 65536 (b) 327680 (c) 131072 (d) 262144
(ii) How many bacteria will be there in 1 hour?
(a) 2² (b) 2⁴ (c) 2⁶ (d) 2⁸
(iii) Write 655360000 in scientific notation.
(a) 6.5 × 10⁸ (c) 6.55 × 10⁷
(b) 6.553 × 10⁶ (d) 6.5536 × 10⁵
(iv) Simplify: (–5)³ ÷ (–5)⁶.
3. A local supermarket, FreshMart, keeps track of sales data using decimal
values for weights, prices, and distances. Below is a snapshot of the data
from a typical shopping day
(i) Calculate the total price for each item in the table.
(ii) Which item in the table has the highest total price?
(iii) Which item has the lowest total price?
(iv) A customer buys: 2.5 L of milk, 1.75 kg of sugar, 3.2 kg of rice.
Calculate the total cost for these items.
(v)A family buys 3.75 L of milk and wants to divide it equally
among 5 members. Howmuch milk does each person get in
litres?
4. Riya is a scientist working in a laboratory to study nanoparticles. She
discovered a particle whose size is approximately 0.00000045 m. To
present her findings, she needs to express this size in standard form using
exponents. During an experiment, she multiplied the size of this particle
by 10⁵ m and divided it by 10⁻³. She also simplified expressions like
(10²)³ and 10⁻⁴ × 10⁶.
(i) Express the size of the particle 0.00000045 m in standard form using
exponents.
(ii) Simplify 0.00000045 × 10⁵ ÷ 10⁻³ using the laws of exponents and
write the final answer in standard form.
(iii) Simplify (10²)³ and 10⁻⁴ × 10⁶, explaining the laws of exponents used.
(iv) Evaluate 2.5 × 10⁻³ × 4 × 10⁵ and write the result in standard form.
