Volume and Surface Area Questions

Circum center of ΔABC is O. If ∡BAC = 75 and ∡BCA = 80 degrees,

then what is the value of ∡OAC(in deg)?

In ΔDEF, G and H are points on side DE and DF respectively. GH is parallel to EF. If G divides DE in the ratio 1:3 and HF is 7.2 cm, find length of DF?

PQRS is a square whose side is 16 cm. What is the value of the side (in cm) of the largest regular octagon that can be cut from the given square?

In ΔABC , DE || AC. Where D and E are two points lying on AB and BC respectively. If AB = 5 cm and AD = 3 cm, then BE : EC is

In an isosceles ΔABC, AD is the median to the unequal side meeting BC at D. DP is the angle disector of ∠ADB and PQ is drawn parallel to BC meeting AC at Q. Then the measure of ∠PDQ is

A cylindrical vessel of radius 6 cm is partially filled with water. By how much will the water level rise if a sphere of radius 5 cm is completely immersed in this water? (Take π = 22/7)

A cuboid of size 50 cm × 40 cm × 30 cm is cut into 8 identical parts by 3 cuts. What is the total surface area (in cm2) of all the 8 parts?

The ratio of curved surface area and volume of a cylinder is 1 : 7. The ratio of total surface area and volume is 187 : 770. What is the respective ratio of its base radius and height?